Is "Forgive my being late" grammatical?
Your example
Forgive my being late ...
is a typical example of a grammatical feature known as a gerund:
gerund |ˈjerənd| noun Grammar
a form that is derived from a verb but that functions as a noun, in English ending in -ing, e.g., asking in do you mind my asking you?. [NOAD]
So, yes, that is a perfectly grammatical expression.
I'd change to to for, but otherwise it seems quite correct to me.
Forgive my being late for this discussion
Any of the following should be acceptable:
- Forgive my being late
- Forgive me for being late
- Forgive my late arrival