I'm not sure about running a 10440 battery in the latest incarnations of the ld01. I think some the newer versions are current controlled instead of PWM regulated.
My Tank007 TK-703, modded to run DD from a single 10440 cell is almost always in my pocket. It gets warm quickly but puts a lot of light out for such a small sized package. It has a decent aluminum SMO reflector so it has a surprising amount of throw for such a tiny pocket light. I try to run it in short bursts only since it gets so hot and I'm sure that DD isn't good for the cheap DX 10440 I have in it.
One of my custom Micro MiniMags with an XM-L driven at 2A and powered by a 14500 making 700 lumen sent through narrow TIR optics. Able to flood a room or back yard and still hit a tree line 100 yds out.
I actually ordered one from them last week. I like my iTP A1 but I wanted an A3 because it's even smaller. And the fact that it uses AAA batteries which is a big advantage if you are going to travel with the light. I plan on using the A1 as my EDC at home and then taking the A3 as my EDC when I travel.
I have a modded solitaire, 1c tint xpg direct drive off of 10440. Pulls 1.7 amps then settles to 1.55 or so. Just a wow light as it gets hot fast. Also have a single rcr123 that pulls 3.4 amps with an xml. Can actually use this for a little while before it gets hot. Has a great beam profile to, more throw than what you would think.