Learn English – What does the phrase “that’s as may be” mean

I never heard this expression before, and it doesn't seem to have much currency today (but see comments below - it's still known to some in the Midlands / north of Britain).

It seems pretty clear to me the meaning is in my life, and I'd guess puff in this sense means something like breath (i.e. - for all the time I've been alive and breathing.

I would not advise using the expression, since many people (not just OP!) will probably not understand it.

Lit is the past tense of light. It means that the stairs did not have good lighting (or more specifically, the person who set up the lighting on the stairs did a bad job.)

The joke is a pun that comes from the fact that lit or lit up can also mean drunk.