If you are checked-in, carry-on bags only, then yes, you can go straight to your next gate.
SATA usually uses buses, Ryanair always uses buses
If you're flying in on FR (ryanair), you'll get dropped very close to the exit from the secure area - you will need to find the stairs to make it back up to the departures level of the terminal (don't go down the stairs - that's the way OUT) and find the non-schengen N gates (10 min walk)
If you are flying with SATA, you'll be dropped off at the far end of the Schengen area right next to passport control for your LGW flight.
You won't need to clear security in either case.
If the flight is on-time (or even an hour late), that's plenty of time to make this connection.