Scrub the potatoes, leaving the skin intact. Add the potatoes to a large pot, and add cold water.
Bring water to a boil, then reduce heat to simmer for about 15-20 minutes or until the potatoes are tender when pierced with a fork.
Drain the potatoes using a colander, and rinse with cold water. Allow the potatoes to cool.
Cut the potatoes into cubes, and place into a large bowl. Add celery, dill pickles, vegan mayo, lemon juice, dill, celery seeds, and salt.
Stir gently to combine, taste, and adjust the salt to taste if needed. Chill for at least one hour before serving.