Do Lewis acids and bases turn change colour of litmus
You should keep in mind that the concept of acid-bases is not restricted to water. Lewis acid definition is applicable to gaseous, aqueous and non-aqueous systems. Consequently, all Bronsted-Lowry acids are Lewis acids. The idea applies to bases. Note that the converse is not true just like an apple is fruit but not all fruits are apples. The idea of litmus test is rather restricted to aqueous systems. So in short, the all relatively strong Lewis acids and bases in water can affect the litmus.
If you put a blue litmus is very dry HCl (gas), it would still turn it red because paper is never dry. It always has moisture absorbed in it.