Gatwick Airport is a Routeing Point (RP)
Watford Jn is an appropriate RP for Luton (for this journey).
Therefore you can travel:
Gatwick-Victoria (any train will do, but non-stop trains every 15 mins are generally empty in the rear coach unless they have come from Brighton so are worth going for) then LU (Victoria Line) to Oxford Circus, then LU (Bakerloo Line) to Wembley Central. Break of journey. Then LO Wembley Central to Watford Jn, LM Watford Jn to St Albans Abbey, walk to St Albans, Thameslink to Luton Airport Parkway.
A variation on that is to take SN to Clapham Jn and then SN from Clapham Jn to Wembley Central, then as per the above.
All the above are subject to engineering work. It will be quicker to do the itinerary offered by W-on-Sea above with an additional ticket (Oyster PAYG is best).