Is this the one you are considering?
I built my workbench out of 2x4's and 2x6's. Some new, some leftover from a previous bench from the 80's.
Lap joints should work great, but not really necessary. But first, I would rip off the rounded corners of the 2x's so you have a finished work piece with square edges similar to S4S (surfaced four sides). That should help with your assembly.
Glue and screws should do the trick. Lay out your boards, square them up with a framing square and screw them together.
Clamps are your friend!
So, all legs should be the exact same length. And any other pieces that are in multiples should also be the same length.
One last thought. My garage floor is terrible. I think the guys that poured our street in the 80's, also poured our slab! Unlevel and uneven no matter where you try to sit something. Shims are a must. All of my tools are on mobile carts or bases and I have to shim at least one wheel before using the tool every time.
Here are some pics of the adjustable height work table/dual router table that I built from 2x4 material. Just as I described, ripped so the boards fit together nicely, glued and screwed.
You can do it!