The proper answer is 'buy or borrow a table saw with a dado blade'.

It would be difficult to safely cut a lap joint on the end of an 8 foot 2x4
using a table saw with a dado blade. Far too easy for the long board to
shift while cutting. Maybe with a proper jig, but I wouldn't try it.

I want to use my plunge router to place a 3-1/2" square lap joint
about 3/4" deep on the ends of several pressure treated 2x4s.
I will don a respirator first, no worries.

A router would work fine, and it sounds like you're alerady set up for the
task.

I don't know what kind of precision you need, but for rough carpentry I
usually "dado" using my circular saw. For instance, if I want to "let-in"
a 1x4 diagonal brace in a stud wall. Just mark the outside edges where you
need to cut, then set your circular saw to the proper depth (3/4" in your
case). Make a cut on each cut line, then a series of cuts in between. For
construction work I usually just use the claw of my hammer to knock out the
thin strips and clean up the joint. If you need a finer joint, you sould
clean it up with a chisel.

Of course, it might be just as easy to make the cut with a handsaw. With a
sharp saw, it shouldn't take more than a few minutes to cut a half lap
joint.

Take care,

Anthony