Is there a way to keep LightBurn from inputing G91 into my g-code output?

I’m not really following your assessment of cause and effect. So curious if something else is going on.

Note that entire job is still described in terms of absolute coordinates. The G0 move before the transition to G91 is described in absolute coords. The relatives moves following that are all relative to that starting position so should be in correct absolute position relative to your origin.

I don’t understand how this could be the case. LightBurn switches to G54 work offset but doesn’t change the offset.

This is where what you’re describing seems to not necessarily follow from how it should actually behave. When using Absolute Coords start from mode in LightBurn there should be no issue in running jobs in terms of absolute position from a machine origin.

You haven’t really described the issue you’re having but based on what you’re saying I’m going to guess that you’re not working in positive coordinates.

Take a look here and see if this applies to you:
Common GRBL/GCode Setups - LightBurn Software Documentation

What do you need and what is LightBurn doing differently from that?