The Lake District is busy from Easter to October half-term and very busy in July, August, and the bank holidays. May and late September are the best windows — long enough days, settled enough weather, fewer crowds. Keswick fills up for the Mountain Festival in May, the Beer Festival in June, the Jazz Festival in May, and the Convention (a long-running evangelical Christian gathering) in late July.
Winter is quieter and atmospheric. Many pubs are at their best in November and February, with fires and short days; the fells get serious in snow and need proper boots, ice axes, and judgement. Rain falls year-round and Borrowdale is the wettest place in England — pack waterproofs whatever the forecast.