Can I move a mech/character with Seaworthy or Submerge onto or off of a lake if they don’t have Riverwalk?

Yes. There isn’t a river between your mech/character and the lake. Think of it like this: If you walk along the shore of a lake, is there a river between you and the lake? Nope. It’s just land, then water. Same thing in Scythe–rivers are between two land territories, while a lake is adjacent to land territories.
Related Rule(s)