Depending on how far apart you allow the "parallel" tracks to be, you might argue:
* The Northern Line Bank Branch is an express service between Euston and Camden Town, while the Northern Line Charing Cross Branch stopping service calls intermediately at Mornington Crescent.
* The Piccadilly Line Terminals (1)23&5 Branch is an express service between Hatton Cross and Heathrow Terminals 2&3, while the Picadilly Line Terminals 4&(1)23 Branch stopping service calls intermediately at Heathrow Terminal 4 in one direction (apart from when it's closed for Covid).
* The Hammersmith&City or Circle Line is an express service between Edgware Road and Baker Street, whereas the Bakerloo Line stopping service calls intermediately at Marylebone. (You might exclude this based on the official Tube map showing the two Edgware Road stations as being completely distinct.)
* [Added in edit:] The Northen Line and Central Line are express services from Bank/Monument to Moorgate and Liverpool Street, as compared with the Circle Line stopping service via Aldgate.
* The Hammersmith&City, Circle, or District Line from Edgware Road to Paddington or Baker Street direct is an express service, as compared with the Circle Line stopping service via Aldgate.
* Potentially similar shenanigans on the Central Line Hainault Loop, going one stop from the split point at Leytonstone either direct or the long way round the loop (not sure if services are/were running all the way round?).