You could start at Piccadilly Circus and walk up to Carnaby street to see its lights. It’s not a long walk and you’d cover both Regent and Carnaby Streets’ lights. While at Carnaby Street, stop into Liberty for its decorations. From there it’s another short walk up to Oxford Street and its lights.
Last year, we stopped to look around Selfridges (decorated window displays) then picked up a regular city bus that took us along Oxford St, past Marble Arch, around Hyde Park, Harrods, and we got off on Cromwell Rd. by our hotel. There are side streets off of Oxford Street that also have lights.
There’s a small Christmas market at Leicester Square, and places like Burlington Arcade and Fortnam & Mason are nicely decorated.
I don’t recall the bus number, but got it from Google maps. It worked well for finding bus numbers at the last minute to wherever we were going. Remember that when taking the city busses, you tap when getting on, but not off. City busses are much less expensive.