Right; you just add definitions you need like
let Y = \f. (\x. x x) (\x. f (x x)) in program-using-Y
which is the slightly more legible version of
(\Y. program-using-Y) (\f. (\x. x x) (\x. f (x x))
let Y = \f. (\x. x x) (\x. f (x x)) in program-using-Y
which is the slightly more legible version of
(\Y. program-using-Y) (\f. (\x. x x) (\x. f (x x))
Also, in lambda calcalus there is no recursion built-in. You have to build it yourself with the Y combinator.