Most of the burns have brownies.
Lamlash specific tips:
The Monamore tends to get fished more than Benlister. Easy parking at the FC picnic area a half mile up the ross road.
There's a bait shop at the pier and boat hire too. The bay is sea loch sort of sheltered. Beach casting on the sandbanks at Cordon(good spot for digging cockles up too). You can cast off the rocks right along at Clauchlands point but mind you're out past the
no take zone.
Never fished anywhere else on the island but seen some impressive salmon out the Lagg(Kilmory Water) down the south end and I know a popular spot in Brodick is down between the beach and golf course where all the burns come together and form a series of tidal channels. Apparently allsorts come swimming up there for a prowl around.