I'm trying to line up my bulb with the triplet.

My bulb is at a 45 degree angle and therefore runs diagonal to the triplet.

I took a picture of the light going through the fresnels that reaches the triplet. It looks like it a little too low and to the left.

Is it just a matter of adjusting my mount to have the bulb higher and more to the right?

Do I need to move the bulb forwards or backwards?

I tried changing it in realtime and seeing the results but I can't tell my eye.

you are right its just a matter of moving your ligth slighty to the right and possibly up a bit

Actually, when making lamp alignment changes with our LL design.
Think the opposite since the fresnels both invert and reverse left for right.

So, in your case to change the lamps offset to center the arc with the triplet. Move your lamp down and to the left.
I know, this fights our natural logic, nevertheless its the nature of muti lens optics.

Also, double check your reflectors alignment. The lip square to your lcd panel and square in virtical pitch. And of course centered to the arc envelop.
Good luck with the tweaking.