LDR Active Preamp - does it exist?

May be you prefer the sound of a little second harmonic distortion, nothing wrong with that, adds a little ease to the presentation if needed, and may cover the sound of the Burson a little, that's what tube amps do.
But if everything is spot on in the system, then the Burson after the Lightspeed will be a more precise presentation, and give warts and all, and not be kind to bad recordings, and let the sound of the Burson through as well. This could be a good or bad thing, I'm not sure how the Burson sounds, but anything active has a sound signature of it's own.

Cheers George

George - to your understanding, is a battery significantly improve sonic quality over wallwart to power Lightspeed?

Thank you George, you nailed it. That's exactly how I would describe the difference between having the Burson before LDA or after, except I couldn't describe it well as you.

BTW, I purchased an empty Burson case to house the LDA and they look great together as a matching pair. The empty Burson case was just about a perfect fit for the LDA to fit inside. The Burson folks are very nice. Typical Aussie's.

The battery is not a significant improvement. There is a difference in the sound but I cannot precisely pinpoint what it is. I swap the power supplies around every so often, but could live with either one.

Same as what Clio09 said, very hard to pick the difference between battery and wall wart.
Even the highly critical listener/reviewer Sam Tellig of Stereophile has memory lapses to what he has on powering his Lightspeed Attenuator when he's using it, as he has both battery and wall wart, and has to look to see which one he last put on, they are so close, same with his guitar teacher son and his Lightspeed I believe.

Cheers George