K40 Whisperer and Meerk40t are generally the most popular programs used to control those lasers.
I’d suggest trying both to see what you like. Meek40t is more flexible but can also be more complex.
You could try running Meerk40t as a intermediary to allow you to control the laser from LightBurn. You could do it during a LightBurn trial period to see how well it works controlling your laser. Normally I’d suggest getting a feel for the laser first to see how it works and behaves, though, so you’re not dealing with too many variables at one time.
Take a look at this Topic starting from this post to get you an idea of what’s involved: