I have a little trouble following your sketch.
Where is the roof vent terminal?

In any case, NO the Lav vent can not be tied into
the stack *below* any toilet. This is not what
is meant by a "wet vent".

The Lav vent must be extended up thru the 2nd floor
to a point above the toilet connection or else
have its own vent thru the roof.

Jim-

Your question of "where is the roof vent terminal" for the lav is
exactly why I find the existing condition peculiar: the 1st floor lav
vent ties directly into the stack *below* the 2nd floor toilet. If
this layout is not the definition of a "wet vent", I think I'll have
to extend the vent up as you suggest (please confirm).

Then, assuming the vent is rerouted and the issue resolved, is there
any restriction you can think of against tying the lav drain directly
into the stack below the 2nd floor toilet per the proposed sketch?