For raw Lift: Lift, NJP, S4~Teleport, F21D2~RUN, S4/F4~Push. It does 27/26% IIRC. You can also substitute the S4 at the end for a F4 for 26%. Just do whichever is easiest for you.
The beginning of the string can be tricky to time correctly. I've noticed that hitting your NJP at the very highest hight of your jump helps you connect the F21D2 after the S4. Also keep in mind that doing S4 ASAP helps a lot as well.
As for F3, I'm at loss as much as you are. I'll usually do D1, Lift, NJP, F21D2, Push. The damage isn't great. But F3 is hardly ever used as a combo starter so I never bothered figuring out optimal combos for it