I am very sorry for your loss, Andrew. May your brother rest in peace. It’s a beautiful idea making your Camino pilgrimage a memorial for him.
Last year I let go of my hopes to walk the full Frances route when I heard that a friend in England was terminally ill. Because of the time frame, like you I decided to walk from Sarria to Santiago (starting out from Australia.)
If you find that flights to Santiago from Gatwick don’t suit you, have a look at Ryanair. As an earlier post said, National Express run a direct route from Gatwick to Stansted: it takes 2 hours 40 minutes (but I’d allow heaps of extra time for traffic!) and 10 times a day; GBP15. For useful Gatwick-Stanstead information see
https://www.londontoolkit.com/travel/gatwick_stansted_bus.htm and for online bus bookings see
http://www.nationalexpress.com/routes/gatwick-to-stansted.aspx
As has already been pointed out, Ryanair flies from Stansted straight to Santiago. Three caveats re Ryanair: it’s only cheap if you book extremely well in advance, and you must keep a paper copy of your boarding pass, because they charged a couple near me a whole heap extra at the airport because they only had their passes on their mobiles! And at Stansted a number of us were confused about the correct Ryanair departure gate: check and double check you’re in the right queue! Their prices are already getting quite high for August, e.g. GBP93 and 79 for 1 August and 7 August; intervening days are a lot more, so book straight away, if you choose Ryanair. They do not fly to Santiago on Thursdays.
https://www.ryanair.com/gb/en/cheap-flights/london-stansted-to-santiago-de-compostela?out-from-date=2017-07-05&out-to-date=2017-10-05&in-from-date=2017-07-05&in-to-date=2017-10-05
Empresa Freire has multiple bus departures from Santiago to Lugo: here are examples for 7 August. (They are on strike at present, with minimal services, so maybe you need a Plan B, just in case: e.g. share a taxi to Sarria.) The tickets are cheap: buy on the bus.
http://www.empresafreire.com/html/ingles/seccion3a.php
At Lugo bus terminus go to the Monbus counter and buy a ticket (also cheap) to Sarria. See schedule:
http://www.monbus.es/en/routes-points-of-sale/123/travel-to-sarria/ You'll be able to walk to your accommodation from the bus station.
Opinions seem to be mixed about whether or not to spend a day in Sarria before starting your pilgrimage. I wish I had: it felt ungrounded to arrive in a place, go straight to bed, then leave at dawn, without first seeing where I had landed! Also, although you will be one of many starting at Sarria, you will be amongst numerous well-seasoned pilgrims who have been walking for days and weeks: I felt such a novice! Do ask other pilgrims for help and information: most will be glad to share their knowledge with you. Pace yourself, and keep well hydrated.
If needed, I suggest you seek advice on the forum about booking accommodation in advance, as it will be peak time…. also about storing or sending ahead excess luggage if necessary, because you'll want to walk as light as possible.
Andrew, all the very best for your special Camino, ‘carrying your brother’ in your heart.