I would check that the MIDI channel in the module matches Ableton,CH 10 is the standard for drums.
Also check and see that Local Control is set to
OFF.
If there is still no MIDI communication download and install
MIDIOXThis will allow you to see if MIDI is being sent by the module to the computer.
EDIT:
After checking around there is also an issue with Ableton 10.1 and Alesis drum kits.
It has to do with note on/off events being too close together.
There is a workaround ,but supposedly the Live Beta program is aware of it and an update is coming
"We have found that as of Live 10.1, any MIDI Note On > Off duration below approximately 100ms might not be captured. The Alesis Nitro mesh and some other devices seem to produce such notes and thus are prone to this.
We're looking into this."
Alesis ForumABLETON LIVE BETAUpdate :
Live Beta 10.1.2 was just released..issue supposedly is fixed
Alesis Forum