Which part of the Lakes? I know the North better but I'd second Hawkshead Brewery - I like their Red Ale. In that area, the Drunken Duck at Hawkshead does great food and brew their own ales. Tag Lag and Chesters are both worth a pint, and you can find their ales elsewhere around the region.
North now, Keswick Brewery Co is in the centre of town and has a tap room. Hesket Newmarket is a village on the northern side of Blencathra and the Old Crown is the site of the community-owned Hesket Newmarket Brewery. Others worth looking out for are Independent Lakeland Breweries , Ennerdale Brewery, and Loweswater Brewery / Cumbrian Legendary Ales who do Loweswater Gold. In all these cases, their beers are sold around the area.