You can, but appart from MU (which requires Max For Live) there aren't many in-depth templates out there for Ableton Live as far as I know.
You can create one to mimic an APC-40 and use the files provided
here to connect it to Ableton. You'll se the red box (or other color, if it's not your first midi controller listed in Live's preferences pane). You'll just have to adjust the MIDI_Map.py file according to what you create in the Lemur Editor, and all should work quite well.
Regarding clip names it's also possible, but unfortunately I don't know how to make it.
On the other hand, there's already
LiveControl for TouchOSC, which works perfectly with Ableton Live, and TouchOSC is quite cheaper. It's also fully customisable, shall you want it.
ST8 (the maker of LiveControl) is working at Liine, so there could be some chance that we'd see a LiveControl port on the Lemur. But maybe I'm just
dreaming out loud.
I was starting to make some sketches of an APC-40-alike template, but compared to LiveControl such a template is quite inferior functionality-wise, so I've decided not to continue doing it and use LiveControl instead.
I'd love to be able to help in a TouchAble or LiveControl type of template for Lemur, allowing full and adaptable control
without the need for Max For Live. I'm missing the programming skills though.