Here's a go at some actual legal analysis of Sony's claims of trademark infringement under the Lanham Act. This is actually an interesting question, I could see it popping up on law school final exams. (Note that this has nothing to do with breach of contract claims like non-compete clauses.)
The first problems will be deciding what exactly Sony is trying to trademark. Is it Kevin Butler's name, his appearance, or his character as a whole? Or, does Sony want to go even wider and trademark Lambert's performance as Kevin Butler in the series of commercials? Since the character in the Bridgestone commercial is not named I doubt Sony would want their trademark to be limited to the name "Kevin Butler." Attempting to trademark his appearance alone may not work either, as it may not be distinctive enough. Attempting to trademark the character as a whole or Lambert's performance as Kevin Butler may run into problems due to overlap with copyright protection, but is probably the best bet Sony has at making a case. However, the closer Sony's trademark is tied to the specific "character" or "performance" of Kevin Butler as opposed to the appearance, the harder it will be to prove that Lambert's appearance in the Bridgestone commercial actually caused confusion, as aside from the appearance of Lambert little is shared between the commercials.
Ultimately from a trademark perspective I don't think Sony has an especially strong case, but it is a lot closer than most people realize.