Chester's Way by Kevin Henkes
By one of my favorite authors, Chester's Way follows two best friends who let in a third friend, who rocks their world and is a fabulous, independent-minded kid. My kids ask me to read it again and again.
My Two Blankets by Irena Kobald; Illustrated by Freya Blackwood
Touching "new kid on the block" story of how kids who may seem totally different from the outside can share a friendship. Tackles loneliness in concrete and specific language that young children will easily grasp.
The Monk and the Yak by Ori Avner
While it seems like a simple story of a cross-species friendship, this story shows that help can come from unexpected places. Just be open and ask!
Say Hello by Jack Foreman; Illustrated by Michael Foreman
Who will notice the lonely kid standing over there? Unique book in that it starts with the dog's perspective (which some children may more easily relate to). This story gives an explicit, easy idea for how to reach out.