Timing is the same whether it hits or is blocked.
-c.LP, close s.MP is a 2-frame link.
-c.LP, far s.MP is a 1-frame link.
Using 2 c.LP instead of 1 means that you’ll be farther away from the opponent thus getting a far s.MP (again, c.LP, far s.MP -> 1-frame link, hard, unpractical in a real match). If you’re having trouble linking the c.LP into s.MP try using s.LK instead of s.MP (it’s alright to use s.MP in block strings but if you’re going for a combo it’s safer to use s.LK instead).
Also, if the 2 c.LPs hit and you don’t have meter you might want to simply end the combo with a HK Somersault Kick. Easy combo, good damage, knocks down.