If you plug a sustain pedal (a momentary on-off footswitch) into the KB GATE of your LP you will be able to sustain the note of the LP (in other words you’ll be keeping the Keyboard Gate open as if you were keeping a key depressed).
But since this is a Control Voltage input I belive this signal is not transmited through midi out of the LP.
I don’t know if there are midi sustain pedals that you could plug into your midi interface and use independently of the LP. Try searching for that.