I too had this problem with a weak bassless sounding DI through a Dynacord desk.
I tested the LM11 DI out at home through my line 6 Toneport and it was fine. I also visited the dealer and tried the LM11 through a different desk - also fine.
I tried it again with the Dynacord using my Fishman Pro DI and it was the same problem. A microphone in the same channel sounded ok.
Eventually to solve the problem we used a XLR /jack converter into the line in and it was much better.
There was no mic/line pad switch on the XLR in on the desk just a level control.
Don't know if this helps.
I think it might.
How are people running this XLR, as a mic or line level signal?

