Penrith and Kendal are only three hours from London by train and so letting the train take the strain is definitely the best way to get to the Lakes. However, unless you want to stay in the busy tourist towns, it is likely that you are going to need a car for getting around in the lake District.
Most people travel to Cumbria by car. If coming from the South you can take the M6 and leave at the exits for Kendal (south and mid lakes), Penrith (east and west lakes) or Carlisle (north lakes). It takes 1-2 hours from Manchester and 5 hours from London to reach the lake district.
Public transport within the Lake District is not great. The main train route runs up the East side of the Lake District and there is a coastal route (slow) that follows the west coast (Barrow – Workington – Carlisle). Travel from London to The Lake District is fast (about 3 hours). Main stations for fast trains are Kendal, Penrith and Carlisle.
Local bus services tend not to be very regular. The main east/west service is the X4/X5 which runs every two hours between Penrith and Workington.
Car hire is available at Carlisle and Penrith.