First off, I think Jesse Eisenberg is a very talented actor and I enjoy a lot of his movies.
to understand my reasons you need to see Lex's character the way I see him (no that I see him better or worse then anyone else. The real reason that Lex hates Superman is that Lex has a superiority complex and all the aspects of his life are based around this.
Reason 1: Being Bald- Now I know some of you are saying, what does having hair or no hair matter to the character but Lex's baldness is a defining characteristic in why he has a superiority complex, when he was younger he felt inferior and embarrassed from his baldness and it is one of the defining reasons why he needs to make himself superior over everyone. Jesse would look terrible Bald.
Reason 2: Muscles- Lex has always been a very muscular guy and In many representations of Lex he is even shown as being more muscular the Superman (not stronger obviously). Lex makes himself extremely physically fit to help himself feel stronger and better then those around him. I cannot picture a ripped Jesse Eisenberg, it could be done, but It would feel weird to me.
Reason 3: Age- Lex should be an adult, he needs to be someone who owns a huge company, fought and done whatever he could to get rich and be an extremely successful businessman. Now I know that this could be done by a young adult as well ala Zuckerberg, but I feel he needs to be someone who has been rich for a while as to be trusted by many americans who will back against Superman, also I feel like someone who has just became rich could not dedicate their new life goal to destroying superman then someone who has been rich for a while and does not need to watch over their company as much any more
Reason 4: Speech- Lex has to be able to make loud boisterous speeches to the public, to superman as superman is almost defeated, hell he even became president. I don't think I could picture Jesse being loud or being on stage rallying an audience to vote for him or to join him against Superman. he would be the more cold calculating type who would quietly tell superman how he's defeated. Another version, but not how I picture Lex.