Gatwick Express

Oops... forgot to ask when we should leave London on the Express to catch a flight to Dubrovnik on April 18 at 12:50pm. Thank you. (U.S. citizen).

Show up two hours before the flight to check in and go through security. The schedule for The Gatwick Express is online on their website.
The Gatwick Express takes Oyster Cards
https://www.gatwickexpress.com/tickets/buy-tickets/oyster-and-contactless

https://www.gatwickexpress.com/tickets/buy-tickets/oyster-and-contactless This is what the website says about Gatwick Express and the Oyster card. The Express takes about 1/2 hour from Victoria Station to Gatwick, so you'll need to factor in travel time to arrive about 2-3 hours prior to your flight departure. It seems to me that the trains leave fairly regularly - if you miss one, you get the next one. They go direct from Victoria out to the airport. That's what we did for a flight to Canada.

Just in case you are interested, there are 'regular' trains that do that same route for significantly less money. They make between 1 and 3 stops and take about 10 minutes longer than the 'Gatwick Express'. During 'rush hour' I think they make more stops and take longer but other than that the regular trains are just as good and you can save a few pounds.

You can but it's a lot more expensive. Book 30 days in advance on the Gatwick Express site and it's not expensive at all.

Thanks, will pirchase my tickets now for April.

There is an discount on purchasing Gatwick Express tickets online, but it is fairly modest (10%). Possibly there is a confusion here with the Heathrow Express.

Where you are starting from in London? Trains from other stations (not just Victoria) go to Gatwick.