Although I also had piano lessons, what you've done with lead sheets is very like how I learned to play by ear.
Different people's brains work in different ways, so I can only describe what worked for me.
Start with simple tunes - Jingle Bells; Happy Birthday, etc.
If you want to develop your skills at working out chords, then start by working out the chord sequence. Otherwise, get the chords from a book or online.
Play the first chord with your left hand. Now play any note with your right hand.
Listen. Is it the right note? If so, good! Otherwise, listen again. Is it too high or too low? By a lot or a little? Use what you've heard to pick a different note to play with your right hand. Keep going until you find the right note.
Then do it all again with the second note.
Every now and again, play the notes you've worked out so far, in the right rhythm. When you reach a chord change, play the new chord with your left hand.
Pay attention to the way the notes fit in with the key you're in, and the chords you're playing. Simple tunes usually only use notes from the scale, so your choice of notes goes down from 12 per octave to 8. Some notes will match the chord you are playing, other notes will be outside the chord. Pay attention to which ones do and which ones don't.
By doing this lots - if your brain is like mine - you'll come to learn:
- What a note sounds like alongside a particular chord -- so you'll be able to pick out a starting note correctly first time
- What the various intervals sound like, and which intervals are particularly significant -- so if you know the first note of a tune, you'll be able to find the second one first time.
Once you are OK with simple songs, move on to more advanced ones. You will come to recognise what makes a tune simple or difficult. If you find that a particular tune is too hard, don't be afraid to put it aside until your skills have improved.