Comment by grumpopotamus

Have you compared the versions of Stockfish in each?

In Lichess I think you can also choose different eval nets. There's a small one and a big one. That will affect N/s.

Have you compared how many threads each are using?

Furthermore, Lichess Stockfish is a WASM build while your local Stockfish is a native binary executable.

Many have already mentioned number of variations will significantly affect time to a certain depth.