Hi Mary,
How about this: Buy either a Visitor Oyster card online (http://content.tfl.gov.uk/english-visitor-oyster-card-leaflet-jan2016.pdf) or a regular Oyster after you arrive in Heathrow. You can then take the Underground "Tube" to London Euston. This will be nice because the lines to buy tickets at the train stations in London can be very long.
Then also ahead of time, buy a return ticket ahead of time for the roundtrip from London Euston to Liverpool. You can do this on the Virgin Trains website: virgintrains.co.uk. This way you take advantage of cheaper fares. I'd give yourself 1hr for immigration, 1:30 to tube to London Euston, 1hr for lunch, and another hour or two just to be safe. Somewhere between 4.5 and 5.5 hours.
On the day you leave, head to Victoria station well ahead of time and visit the Travel Information Center to get a refund for the fee you paid for the Oyster card and any unused balance. If you buy the visitor Oyster, you don't get that fee back.
I bought the regular Oyster and got a refund on my way to Eurostar in London last fall. It worked really well. Oyster cards have daily and weekly caps, so even if you do end up riding a lot of trains while you're in London, it will max out at a similar price to a travelcard. Also, I preferred riding the double-decker buses anyway. They're cheaper and have a great view from the upper deck.
Good luck!
Nordheim