With a lambda expression you'd still need to recursively check each character of the string, or you could use map which is still a recursive function that applies the function (a -> b) to every element in the list, for example:
newList [] = []
newList xs = (\(y:ys) -> if x `elem` ['A'..'Z'] then toLower y : newList ys else y : newList ys) xs
With map is actually much simpler due to reasons explained in the first paragraph, check mnoronha's answer as he already gave you the answer, but that's if you're thinking of using map in conjunction with toLower.
This is an example without a lambda expression, which requires you to import 2 functions from Data.Char, recursively check the rest of the string and replace each character with its lower case version.
newList :: String -> String
newList [] = []
newList (x:xs) = if x `elem` ['A'..'Z']
then chr (ord x + 32) : newList xs
else x : newList xs
or with guards
newList :: String -> String
newList [] = []
newList (x:xs)
| x `elem` ['A'..'Z'] = chr (ord x + 32) : newList xs
| otherwise = x : newList xs