I'm finishing my basement and I've come across this lally column which is supporting a steel beam. I want to frame an external corner for this interior wall at this "corner" but the distance from where the back of the drywall would be to the column (especially on the right side) is really small, like maybe 0.5"? Since I can't fit a 1x1" there, how do I frame this corner?
Here is my suggestion. It is only part of the post in the drawing, but it is the same all the way up, the scrap pieces of plywood are about 1 ft apart 3 or 4" wide, can be wider, can be solid, done that too. Makes for a really strong corner for corner bead. If you don't use 1/2" plywood and need to use 1/4" it will still be really strong. Using a full piece of plywood makes a straight corner really easy. It is what I do, I shown pieces so the method of construction is seen. I have also used 1X and had good results too, I use glue to help hold it....
Use plywood as the corner material for both sides. The corner can be built on site and installed when complete. Strengthen the corner with brackets installed on the inside and construction adhesive. You'll need nailers on each end of the attachment walls.
You could also just extend the drywall without framing since the distance past the framing is minimal (glue the two pieces were they meet at the corner).
Don't frame it, just wrap the ends of the walls with drywall to behind the column & paint the column to match or contrast. Or, you can make it decorative & give yourself room to boot. Screw a 2x8 & 2x10 into a corner with corner bead (guessing what it is to each end stud), then screw those flats to the wall end stud faces (only half the width of those studs so drywall can lay & screw)...Bumps-out just the corner (2" with drywall, if desired). It would look great & you can corner bead the bump-out to get all 3 corners sharp.
Option 1 leaves the column accessible, but possibly difficult to mud & corner-bead. Option 2 could be removable with just screws at the very top & bottom...if desired. Pre-drill both the lumber corner & the wall studs so you don't split that 3/4" you'd screw Option 2 into.