The issue on microlights is not who can maintain the engine (anybody can), but who can certify that maintenance. In general it needs a signature from whoever did the work, and a second signature from one of (a) A BMAA inspector, (b) the owner, if it wasn't them who did the work, or (c) another PPL if it was the owner who did the work, or (d) the aircraft manufacturer.
The LWTR or equivalent clearly means you'll probably know what you are doing (that said, I doubt the course covered 2-stroke engines in any great depth), but gives no special privileges in the BMAA system.
I agree with Cubflyer about asking the BMAA, but there is also a lot of information on their website which may contain the answer. Try Technical Information Leaflet 020.
P