Now, if you already have favourite dry mayfly patterns for the rivers they'll most likely do fine for lochs and lakes. The Wulffs are a great example of a style that crosses over well, yellow olive and grey being my favourites. There are of course some that I don't think transition as well; Ollie Edwards' Mohican mayfly makes an excellent, high floating pattern that works great on rivers and it will catch fish on stillwaters. Unfortunately, I've found it to be a less effective hooker on the lochs- I suspect the fly being essentially static or gently drifitng with the breeze rather than drifting quickly past the fish on a river eliciting a different eat that is the reason.
Similarly there are some patterns that are probably better suited for lochs and lakes than they are rivers. The rollover may style (main picture) that Patsy Deery came up with is one such style, again it will certainly catch on a river, but it comes into its own fished in front of a drifting boat. On a shortish line the oversized wing will catch the wind and cause the fly to flip and roll- much like a newly emerged dun struggiling on the surface. If you have a suitable rod and some floss, it makes a great dapping fly, as does Peter Dean's shadow mayfly. It's maybe less popular now than it once was, but that's got nothing to do with its effectiveness.
The last type I wouldn't be without are the flies that can be fished wet or dry. The Irish style stimulators are, to my mind, far and away the best choice for these. The deer hair wing and tail when greased up make for a very buoyant offering that makes a great point fly for suporting a couple of nymphs or emergers on the droppers, much the same as using a booby for the washing line technique. When the fly eventually gets pulled under it can be retrieved back and makes a fair impression of a nymph making its way to the surface. They're a great choice for those days where the fish seem to be a bit non-commital when shown other dry flies, that barely subsurface presentation can often elicit some very aggressive takes.
All this has got me rethinking where to go this summer,I was hoping to make it to Okinawa if the pandemic situation allows, but maybe I'll head to hokkaido for some lake fishing instead.