Come on, that's only true for one of them. Lovren certainly jumped at the first opportunity and so we treated him like the mercenary that he is.
Lallana must have had plenty offers from other clubs as soon as we were relegated into League 1, and after five years it's only natural he might want to move on. I think the vitriol rose from expectations from interviews disingenuously talking about "becoming the next Le Tissier".
Lambert had major interest from West Ham as others have pointed out, but as he made clear when he left, he wasn't interested in joining another club other than Liverpool. Had Osvaldo been a hit (in the goal-scoring sense) I'm sure he would have been moved on sooner.