Is there an easy way to see all of the programs a specific lead is currently a member of?
One way to achieve this can be by the use of API's or by creating a people performance report and grouping it by email address ( in the smart list you use the step of member of program true and program filter name)
Sanford Whiteman sir, could you please suggest any better option here please.
I agree with your suggestions, not really any better option unless you maintain a field on the lead that holds all the current program memberships (this requires a webhook to prune/dedupe the list, so not a very common tack).