We had a similar situation with Modric. Fans called him a traitor. He attempted to leave but we forced him to stay one more season (and he played some of his best football) then got his move. Most fans still slate him but I wasn't one of them as Modric (like Lallana) played with determination and passion when picked. Modric also signed a contract, declared he was happy and a year later attempted to move but he wanted to better himself.
Lallana has decided to better himself and there was no easy way out. Fans are just sensitive but you're right to remember him for the quality he showed, as he gave his all when picked and believes he has outgrown Southampton.
The only Reason Lambert is viewed different is because he is seen as loyal. He had no choice to be loyal. First chance he gets(and last chance) and he takes it but Lallana can't sit around until he's 32 just to prove his loyalty and leave on good terms.