Davies, 21, made 14 appearances in first-class cricket for the Red Rose last season, scoring 730 runs.
England Under-19 international Parkinson, 18, is yet to make his senior debut for the county.
Lancashire finished second in Division Two of the Championship in 2015, and also won their first T20 Blast trophy with victory over Northants.
"Alex is an exciting talent and is very much a key member of our squad - you almost seem to forget that he's only 21," director of cricket Ashley Giles said.
"With Jos [Buttler] being away with England, Alex has stepped up and made excellent contributions not only with the gloves but also with the bat.
"Matty is another talented youngster we have at Lancashire and he will play an important part for Lancashire in the future."
Lancashire have agreed new contracts with wicketkeeper Alex Davies and leg-spinner Matthew Parkinson.