You don't say whereabouts in the Lake District - BUT - as an example...
Shrewsbury to Kendal is a distance of 127 miles, and would take roughly 2 hours, 40 minutes to drive - according to Google Earth.
6 hours drive from Nottingham
The shortest time is 2 hours and 36 minutes.
The drive time from Salt Lake City, Utah to Washington, District of Columbia is:1 day, 8 hours
About 4 hours, or perhaps 5 if you have to drive from S.E. London.
3200km long
The Lake District is about 54 km across (west-east) and 48 km long (north-south).
The Lake District is quite large and times may vary. From London to Lake Windermere is about 4 hours and 30 minutes without stopping, using the M1 and M6.
About six hours
How long does it take to drive from St. Louis Mo to Lake Florida
Carlisle is on the edge of the Lake District so no time at all.
Google Maps estimates the driving time as 7 hours and 49 minutes.
The drive from Salt Lake City, Utah, to Lake Tahoe, California, is 8 hours long. Most of the trip involves driving through the state of Nevada.