That has been suggested, but it's such a good idea, I'm glad the notion has more voice.
I'm not sure if a location for such a thing has been suggested, but my two cents: decrease the size of the in-hand card thumbnails (which I think should be done, regardless; it's irksome, having to scroll), and add an icon allowing you to view a list of previous actions.
I'll bet your losing of cards is due to Lillian's Corrupt ability.
As an aside:
In paper Magic parlance, what you're suggesting is essentially the graveyard, though that doesn't cover recently-used abilities, what with there being no paper to place in the pile.
Just in case you didn't know.