I'm not sure if it is possible to cycle out of Heathrow (central terminals) at all.
Assuming they are arriving at Heathrow with a bike box, I'd really just recommend getting a taxi all the way.
If they are staying in central London before the ride, then Piccadilly line (heathrow express costs a lot more for a half hour time saving), note this would need a boxed bike.
Heathrow express will take full bikes. as will the circle line so this is really the best bet if bike is assembled and bike box left at heathrow.
Cycling between Paddington and Liverpool street is mostly ok on good infra except the first bit from Paddington to marble arch (marble arch, hyde park corner, Trafalgar square, embankment) (marble arch, buckingham palace, tower of London/tower bridge not far off route so good sightseeing)
I would not advise anyone to attempt to cycle from central London to Debden, the roads heading out that way are quite unpleasant, and the off road routes not especially secure for the ingle traveller with an expensive bike