No, it's not true.
To start off, "Alice in Wonderland" wasn't a planned story. It was something he made up as he went along, which is why it's so random and illogical. He told it to the daughters of a family he was friends with during a boat trip, so he didn't have any type of writer's block. Quite the opposite, actually.
LSD hadn't even been synthesized during "Alice in Wonderland" or its sequels time. The first book was created in 1860, the second not too far after that. LSD was first synthesized in the 1930s, and became especially popular during the 60s.
His work may seem very trippy, but it's not because he was on drugs. He was just a very creative man. : )