From Dehradun you can take bus to Kotdwar and from there take cab or taxi to Lansdowne. Or if you don't get the bus from Dehradun then try to reach Rishikesh you will definitely get the bus to Kotdwar from Rishikesh..
The total distance between Dehradun and Lansdowne is 155 KMS. almost via Nimbuchaur - Haridwar road. And 138 KMS. via Gumkhal - Silogi - Rishikesh road.