Here is the LEGO build of a sound activated version. This is the underside. Same struts/tracks up front and motor config as the Mounting Board version. You can see here that I used the Mix module to complete the motor circuit. This is only to flank the motor for strength, as mentioned above. I used Mix only because my other options were in use. I do not suggest using Mix
The topside of that quick LEGO build. This uses the LEGO Ninjago Thunder Raider kit (70723). It's a solid deal because it is actually two models, has the right wheels, cool tracks, and mini figs.
Keep in mind, the Mix module is only there because I needed the one sided ends for motor flanking and my other connecters were in use.
Which gets back to the original point of this thread. The adapters in the full LEGO result in a fairly "loose" build. Granted, this example is using a minimum of blocks. More blocks would strengthen the LEGO parts. The interface with littleBits is going to require patience and extra care though, due to the fit. Just have children take their time, and lend them a hand when things start to get wobbly. Finally, don't feel that you have to only use LEGOs and litteBits. If you have to gaff something to keep it from falling apart, have at it
Oh, an IMPORTANT note on drive wheels. It might be easier just to get wheels with 3mm axles (Iike Pololu #1088 - as suggested in the Robot Butler build). The LEGO wheels you need are the ones that take the LEGO axle shaft (LEGO 3707) directly. This includes LEGO 56145 (use Brickset.com to find kits that have these). You may want to check out Pololu 1011 (shaft adapter) as well. I have not yet tried it, but if it works, it would reduce the length, and subsequent side load, of a motorMate plus an axle (even the short, notched 32062 - which is pretty perfect)
Here is a link with rims and their axles:
A quick note regarding Gaffer tape (think of clouds parting & angels singing in joyous recognition of this tape). It is NOT duct tape. It is pricey, but very re-usable for maker projects. The tape is easy to remove and the adhesive will not remain on your LEGO or littleBits components. I prefer a 2" wide roll. It is fairly easy to tear once you have the hang of it, thanks to the cotton construction. So making narrow strips is quick work.
...and I believe I am done now. Sorry for all the edits.