I take it the OP is referring to Natalie Lallana, Adam's sister. I confess I didn't know she was playing in this tournament. However Adam Lallana has, if anything, played better for England than I have seen him play for Liverpool. He has two problems: first, his finishing is not good enough, this is not a recent problem but has been evident for some time; second, he seems to run out of steam very quickly after half time, so he really is only up to delivering 45 minutes for the team.
It isn't happening for Kane at all; whether this is because he is exhausted from the season with Spurs, because he is not getting the service he requires or for other reasons I don't know, but his performances on the pitch so far in this tournament would not merit a starting place in the team. But then none of our attacking players have consistently hit the back of the net or looked like doing so (Sturridge/Vardy looked good against Wales, nothing special at all against Slovakia). I'm inclined not to refuse to pick them all, but to persist with them in the belief they will start converting the chances they are given.