I have an incoming L2K Tribute.I use a basic 3 pedal setup with my L2K consisting of Compressor > Overdrive > Chorus. I had to make some fine adjustments, but for me having the compressor first seems to be a good thing. Also, I backed off the volume knob on the bass just a tiny bit which also helped. Overall, my L2K and my pedals work and play very well together.
Got a board with 12 pedals. I have HPF/LPF always on near the end of the chain, and a BBA buffer at the beginning. I boost the signal with BBA for my P bass and my Stingray, so I can easily back that off for L2K. Hoping I can tame the output a bit with HPF/LPF if it proves too hot. I find that usually it's the low end that clips inputs, but I can always back off the onboard L2K controls. Maybe the L2K's signal output will be on par with the boosted signal I do for my other basses, that would be perfect.