Not living in England and not having daily exposure to all types of 1st class cricket makes it difficult to know who's hot and who's not, but I'll give you three names to replace (for the next two series against Pakistan and South Africa) the above mentioned failures.
Alex Hales in for Lyth.
James Taylor in for Bairstow
Gary Ballance in for Bell. KP is an option, but the powers that be - Strauss - means he will never play for England again.
Lyth and Bairstow undeniably have form in county cricket don't have the technique nor application needed at Test level).
Lyth - opening batsman: 6 Tests, average 21.45
Bairstow - lower middle order batsman: 16 Tests, average 28
Simply, it's not good enough.