Hi Rebecca and welcome to the forum.
I have no experience of walking or wild campling on Anglesey but I do have a bit of experience of wild camping in the Snowdonia area, and as I am not getting any younger my walks and wild camps are becoming at low-to-mid levels as opposed to away from it all up in the heights. Consequently I am more often looking for somewhere to pitch in areas with cottages, farmhouses and grazed pastures.
Nevertheless, there are always rough, ungrazed spots where you can hide yourself away without anyone knowing you are there. Behind a wall, or a ruined building, behind a slight rise in the land, that sort of thing, but I don't mean literally behind them, you just need something in the line of vision between you and watchful humans. The other side of trees or bracken would do as well.
What I think you need to avoid most is pitching in any grazed field, which I suspect any farmer would react angrily to. What you need to try and find out about Llyn Alaw is whether there's any dry land around it, as so many Welsh lakes turn out to have boggy surrounds.
I write this having just returned from a trip to north Wales, the most recent of many over the years, where camp #1 was behind a high wall next to a footpath, #2 was in view but on a bit of rough land next to sheep pastures where I am sure no-one would have objected, and #3 was 100m from a track and hidden by trees and shrubs. You might have heard of the "arrive late and leave early" advice, well that doesn't apply to me, I arrive around 18:30 (it's light till 21:00 in north Wales at the moment) and I don't get up before 07:00 and take hours before I depart. In the event, I saw absolutely no-one at each site.