Ok, so i am probably worst person to answer that, because i have never did a single combo on real match (in training mode, sure :D ).
Secret to comedy and combos, it's all about timing.
With links, you have to input next move, in the moment when animation of previous move ends.
So you have to wait a bit.
With Ryu lp > lp ~~ mp, you have to do in rhythm: BAM BAM wait for it BAM.
Set dummy to autoblock, and try that.
If move don't come out, you are doing it to fast (looks like this: lp comes out, lp comes out, you press mp and mp doesn't come out)
If dummy blocked, you're doing it to slow (looks like this: lp comes out, lp comes out, mp comes out but dummy blocked).
You have to find this moment between this two speeds.
I can link some video guides about it, but thats basically it.
And, i use Ryu as example, but combo lp lp mp xx special works on (i think) every character, with small adjustments (sometimes only one lp, sometimes lk, sometimes mk, you can google it or test it).
I am a lame player, but i am trying to git gud, so i know few things - I will by happy to help :)