Euston may not be on the Piccadilly line but King's Cross - St.
Pancras station is very close to it. I would suggest you get on a
Piccadilly line train from Heathrow (completely step-free) and just
stay on all the way to King's Cross - St. Pancras. There you go up the
escalator and walk to the exit. From there it's a very short 5 minute
walk along the Euston Road to Euston Station. This saves you the extra
interchange with your luggage, and it's probably faster than changing
again anyway.

Here's the walking route, it's 0.4 miles according to Google.
http://tinyurl.com/cafjty