Yes, Spike Lee should endorse Sanders, if Spike Lee feels the urge to do so. All Americans have the right to free speech. That right should not be restricted for anyone. If someone like Spike Lee, a well-known film director, wants to endorse Sanders as a presidential candidate, Mr. Lee has every right to do so.
Spike Lee, as with any other person in this country, should support who they feel is the best candidate. I don't even think that celebrity endorsements are even relevant. I have never seen a celeb endorsement that has made me think twice about my candidate of choice. Simply put, every person needs to make their own choice, regardless of what others think.
Spike Lee should not endorse Bernie Sanders. When celebrities endorse politicians, many young people vote for the endorsed because they have no other basis on which to vote. Instead of endorsing candidates, celebrities should use their influence to encourage young people to research the candidates before casting their presidential votes.
Only Spike Lee has the experience and wisdom that comes from being Spike Lee, so I can't say what he "should" do. It would probably be a small boon to the Sanders campaign, and wouldn't cost him anything, so in that sense it would be a good move as it pertains to Bernie. But Lee has his own important issues that are knowly only to him.