The big issue is getting through immigration and customs at LHR. If you can somehow cadge a Fastrack card from a FA, you can get through immigration in less than 10 minutes after entering the immigration hall (depending on where your plane parks, you can have at least a 10 minute walk from the plane to the immigration hall). Otherwise, plan on one hour clearing immigration and customs.
The tube will take around 50-55 minutes, with a change to the Northern Line at Leicester Square. If you have a rail pass, use the Heathrow Express (15-20 minutes), and at Paddington look for the Hammersmith line which will take you to Euston Square, about 400 yards from the entrance to Euston Station, about 20 minutes total.
So, if you are going to buy a discount ticket and book a certain time to leave Euston, the time should be at least 2 hours 30 minutes after scheduled airline arrival.
My experience with this is that once a year I fly into LHR and take a train from Euston to Glasgow Central. I am a big fan of Britrailpasses. If you haven't thought about buying one, really look into it.