Hello Francis,
From Dehradun to Lansdowne, it'll take you around 4 h 29 min (157.1 km) via Nimbuchaur - Haridwar Rd and NH534. You can check out Google Maps and figure out the road.
Take a bus for Kotdwar from ISBT Dehradun. There are several bus for Kotdwar from Haridwar bus stop also. Lansedown is about 35 km from Kotdwar, tak a taxi or regular bus from Kotdwar to Lansdowne
The total distance between Dehradun and Lansdowne is 155 KMS. almost via Nimbuchaur - Haridwar road. And 138 KMS. via Gumkhal - Silogi - Rishikesh road.