Personally, I'd drop Lyth like a stone. I understand that wholesale changes are not a good thing, so I'd much rather retain an out of sorts Ian Bell than Lyth, who simply doesn't look test class in any way. Bell, on the other hand, is a decent enough batsman suffering a bit of a wobble.
But...
I fairness, Broad has just bowled himself into a bit of form against Yorkshire. I don't like Stuart Broad much but would prefer he got the nod over Finn.