I have come across two ways of studying melody. First way is with structural tones(melodic outline) and second way is with chords(chord/none-chord tones).
I assume considering melodic outline is only when chords are not available. Then, when there are chords present in a lead sheet, considering melodic outline really necessary?
Theory on melody is not as well covered, and easily available, as theory about harmony. So, if you want to get into studying melody, take time to build up a good collection of resources.
However, this much should be said about your question: it is not an either or case. Rather that choose analysis by chord tones or structural tones, as if those are mutually exclusive, you want to use both analysis tools.
When you say "lead sheet" I assume we are taking about melodies in a homophonic style. That is, melodies that could be harmonized with chords. If you are analyzing such a melody and there happens to be no chords given, you can, and probably should in many cases, analyze the melody according to its harmonic implications.
Analyze the melody. Lead sheets are not that good in general. If you get the melody analyzed, you may find more than one possible harmony.
A good (very old but the principles still apply and there is a free pdf) book on melody is Geotschius' "Exercises in Melodic Writing." It's good for most songs. Once you get the basics, you can expand as your ear tells you.
