The law regarding discrimination by private parties is found in Sections 2 and 5 of the Fourteenth Amendment.
[N]or shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws. . . The Congress shall have power to enforce, by appropriate legislation, the provisions of this article.
U.S. Const. Amend XIV.
The Fourteenth Amendment was passed after the Civil War to curtail slavery.  Most Constitutional law is determined and written by the federal courts, but some things, like enforcing equal protection, and regulating Indian Tribes, are left up to Congress.
Congress has passed many landmark laws interpreting the Fourteenth Amendment including:
1. The Klu Klux Klan Act of 1871,
2. The Equal Pay Act of 1963,
2. The Civil Rights Act of 1964, 
3. The Age Discrimination Act of 1967,
3. The Fair Housing Act of 1968,
4. The Americans with Disabilities Act of 1990,
5. There are lots of other 14th Amendment enforcement acts.
Of course, the federal courts interpret what these statutes mean, they just have to treat each 14th Amendment enforcement statute as if it is itself part of the Constitution, and cannot invalidate any part of it.  
When evaluating the rights of an employee who is discriminated against by his company, we have to ask:
1. Is the discrimination against the employee based on his race, color, religion national origin or sex? (From Title VII of the Civil Rights Act).
2. Is it because he is old?
3. Is it because he is a woman?
4. Is it because he is disabled or pregnant?
If no to all, then its probably okay.
Although it gets kind of gooshy, the Equal Protections Clause only protects a person based on who he is, not on what he does.  Private Americans routinely discriminate against the poor and those who show criminal tendencies.  
Now, Doc's question is about Due Process.  Should a person be shown some degree of due process in disputes at his workplace?  The only federal law controlling how Employers treat all employees that I can think of is the Fair Labor Standards Act of 1938.  The FLSA is made under Congress' power to regulate interstate commerce, and not under the Fourteenth Amendment Due Process Clause.  The FSLA covers thing like minimum wage and the 40 hour work week and does not apply to millionaire football players.
The Fourteenth Amendment Due Process Clause generally only applies to state governments, and not to private parties.  Is your kid being expelled from school without the principal hearing his side of the story?  Due Process case.  Did your boss fire you for your Facebook beer bong picture?  Private problem, no federal case.  Did your boss fire you because he heard of your Ramadan fast?  Equal Protection case.
This is the law.  Is it just?  
I think that a companies' desire to dissasociate from a certain person is okay.  A company has its own Constitutional rights, including Freedom of Association, and Freedom of Speech.  If an employee does something that tarnishes the brand image of that company, the company has a right to dissasociate itself from that person, as long as it is following the Equal Protections enforcement statutes outlined above.
Here, The NFL is confronted with the footage of a player knocking his girlfriend unconscious and dragging her body from the elevator.  This sort of footage is not endearing to female fans, its sponsors, or the general public, and has diverted attention from the on field product that the NFL is trying to promote.  Did Ray Rice owe the NFL a hearing before he cost it millions in revenue and goodwill by his act?  A company has a broad ability to dissasociate itself from unprofitable people in a free market.

To put it another way, what did the Baltimore Ravens ever do to deserve this?  
 
 
 
 

Yeah Doc, this isn't legal territory at all.  But, you've drove me to it:  Here's what the NFL Collective Bargaining Agreement of 2011 says:  Credit Forbes for getting me started:
All disputes involving a fine or suspension imposed upon a player for 
conduct on the playing field (other than as described in Subsection (b) below) or involv­ing action taken against a player by the Commissioner for conduct detrimental to the integrity of, or public confidence in, the game of professional football, will be processed exclusively as follows: the Commissioner will promptly: send written notice of his action to the player, with a copy to the NFLP A. Within three (3) business days following such written notification, the player affected thereby, or the NFLPA with the player's approv­al, may appeal in writing to the Commissioner
CBA 2011 Article 46 § 1.(a)
The Collective bargaining agreement then lays out a complex arbitration process that is similar to a court trial and appeal procedure for disputes of this kind.  
Forbes argues that NFL CBA domestic violence abuse guidelines set down by Goodell himself, the Promptness Clause of Article 46 § 1 and the Double Jeopardy Clause of CBA Article 46 § 4, as well as settled arbitration principles preclude a lifetime ban.  
The Goodell sentencing guideline is a memo that Goodell allegedly sent to owners stating that players would get a six game suspension for a first DV offense.  The CBA double jeopardy clause reads as follows:
The Commissioner or a Cub will not both discipline a player for the same act or conduct.  The Commissioner's disciplinary action will preclude disciplinary action by any Club for the same act or conduct.
Nothing in Article 46 says that the Commissioner gets to impose discipline on a player twice, and, if there was a 6 game guideline in place, then Rice may have something in arbitration.  It should be noted that the fact that the NFL has a double jeopardy clause has just joined my long list of reasons why I don't enjoy football games.
 
Now, about external pressure.  A group determines how important public pressure is to it.  For profit organizations generally have more of an eye to public pressure than not for profit organizations.  A church generally is more insulated from outside pressure than a company, but it doesn't mean that the company is wrong for caving to public opinion.  Think of it from a product angle:  
Steve Jobs thought that a large screen smart phone would never sell.  Tim Cook and the board of Apple decided that they were tired of losing their cellphone market to Samsung and LG, and so they changed up their product to include an iPhone 6,(big) and iPhone 6+ (Bigger).
The NFL is doing the same thing.  Ray Rice, like the four inch iPhone, has fallen out of public favor, and it is costing the NFL money.  Therefore, get rid of Ray Rice, problem solved, crisis averted.  This does seem kind of chicken, and it does violate the NFL's branding of itself as the league of rules and not men, but it doesn't seem too extraordinary given the circumstances.

Here's what's probably going to happen:
Rice goes to arbitration.  The arbitrator either reduces the lifetime ban to 6 games based on the Goodell memo, or 2 games based on the double jeopardy or promptness clauses of the CBA, or uses some other NFL precedent we don't know about (Arbitration is secret) and then Rice will be out looking for a job, as the decision by the Ravens to cut Rice will still stand.  He then signs with some other team, or no team will sign him and he is blacklisted.
Goodell then states that he disagrees with the arbitrator's decision, and he gets to blame the arbitrator for enforcing unpopular NFL policies and the CBA.  What is wrong with this picture is that Goodell is supposed to uphold the CBA and NFL policies.  It is his job.  If the lifetime ban is clearly contrary to the CBA and NFL arbitration precedent, then he isn't doing what is right.  Also, your point about caving to public pressure regarding employee discipline is very convincing.  If there is one thing you shouldn't cave to public pressure on, it may be that.
Thanks Doc for a good philosophy dispute.

It's mind boggling how poorly the NFL has bungled this. It *should* cost Goodell his job. They give a Rice a two game suspension...then once they see the video (supposedly), they punish him some more? What exactly did they think happened in that elevator to render her unconscious? Or did they just think that the video would never become public?
Goodell looks every bit the weak kneed weasel of a company man that he is. No way the NFL can be led by a guy like that.

"I had more when I was in the bathroom, let's see if I get them back."
I Hear Ya, Ice.
No, no...NOT in the bathroom.
I hear ya about losing good thoughts and wondering if you'll get them back. I guess once we get to that point most of the time their just gone forever.

Thug behavior (or the perception of thug behavior) seriously wounded the NBA and it hasn't really bounced back to peak popularity.