I am looking to mount a pull up bar to the bottom of a beam in my basement. (it is unfinished, as it is a brand new home)
I have two main beams going across my basement, opposite direction of my floor joists. The beams are made up of two
laminated 2x10's nailed together.

My question is... can I screw in two lag screws to the bottom of one of these 2x10's (the 2" bottom side, when looking up) to
mount my pull up bar. And I would also do this closer to an outside wall, not in the centre of my basement. Or is this against
code/just not a good idea - and try to mount using my actual "I" floor joists...

Thanks for any advice!

You can install your pull-up bar anywhere on those beams. The lag bolts are not enough to weaken it. As for load, those beams are designed to hold the dead-load of the floor framing as well as any live-load that may be walking around above. Your weight hanging beneath the beam is no different than if you were walking around (or jumping) from up above.

The beam is a much better point to attach your bar vs bolting on to the I-joists. You can use the I-joists, but you need to carry the load from the top of the I-joist, not the bottom run. This can be done by framing either 3/4" plywood or 2x material from the top cord of the I-joist to the bottom in the area that you would mount your bar.

But again, it will work fine with no modifications if you attach to the underside of either beam.