How long does it take to get to the lake district from stepney green station, london?

It depends on the method of transport you use.
if you're driving go onto and check the route, it'll tell you the distance and time the journey will take.
Yes also check out does same as above.
By car - give yourself between 5 - 6 hours. We did it overnight, and by taking it steady, we got there from Barnet in just over 4 hours.
Summary: 289.7 miles (4 hours, 38 minutes)

09:000.0Depart Bethnal Green Underground [Three Colts Lane, London, E2 6, United Kingdom, Tel: +44 20-72221234] on B135 [Three Colts Lane] (West)0.2 mi
09:010.2Turn RIGHT (North) onto B108 [Vallance Road]0.2 mi
09:020.4Turn LEFT (West) onto A1209 [Bethnal Green Road]0.6 mi
09:041.0Turn LEFT (South) onto A10 [Shoreditch High Street]54 yds
09:041.0Continue (South) on Local road(s)43 yds
09:041.0Turn RIGHT (North-West) onto A1202 [Great Eastern Street]0.1 mi
09:051.2Bear RIGHT (North) onto Curtain Road0.2 mi
09:051.4Turn RIGHT (East) onto A5201 [Old Street]0.1 mi
09:051.5Turn LEFT (North) onto A10 [Kingsland Road]5.0 mi
09:166.4Bear LEFT (West) onto A109 [Lordship Lane]142 yds
09:166.5Turn RIGHT (North) onto A10 [The Roundway]1.5 mi
09:198.1At roundabout, take the SECOND exit98 yds
09:198.1Exit roundabout onto A10 [Great Cambridge Road]5.0 mi
09:2913.1At roundabout, take the FIRST exit32 yds
09:2913.1Exit roundabout onto Ramp0.4 miM25 / A1(M) / M1 / M4 / Watford / Heathrow
09:3013.5Continue (West) on M2515.1 mi
09:4228.5At M25 Exit 21, bear LEFT (West) onto Ramp1.1 miM1 / The North / Luton Airport
09:4329.6Bear LEFT (North) onto M12.6 mi
09:4532.2At M1 Exit 8, stay on M1 (North)6.7 miM1 / The North / Luton
09:5138.8At M1 Exit 10, stay on M1 (North)52.2 miM1 / The North / Luton / M Keynes
10:3291.1At M1 Exit 19, continue (North) on Ramp0.8 miM6 / The North West / Coventry (North) / Birmingham
10:3491.9Continue (West) on M636.0 mi
11:02127.8At M6 Exit 8, stay on M6 (West)103.0 miM6 / M1 / M40 / London / Birmingham (N. E. and Cen) / N.E.C. and Airport
12:25230.8At M6 Exit 32, stay on M6 (North)31.2 miM6 / The North / Lancaster / The Lakes
12:49262.1At M6 Exit 36, continue (North) on Ramp0.2 miA590 / A591 / A65 / South Lakes / Kendal / Barrow / Kirkby Lonsdale / Skipton
12:50262.3At roundabout, take the FIRST exit10 yds
12:50262.3Exit roundabout onto A5903.5 mi
12:55265.7Continue (North-West) on A5914.9 mi
13:02270.7At roundabout, take the SECOND exit174 yds
13:03270.8Exit roundabout onto A59110.3 mi
13:19281.1Bear LEFT (North-West) onto A50950.5 mi
13:21281.6Bear LEFT (North) onto A5932.1 mi
13:25283.7Turn RIGHT (North) onto B53433.8 mi
13:32287.6Turn RIGHT (North) onto Local road(s)2.1 mi
13:38289.7Arrive Lake District National Park
By train - Hammersmith and City line to Euston Square. Short walk to Euston, train to Oxenholme. Say 4 hours roughly. Allow a bit longer for connecting train to Kendal & Windermere.