No, lactose intolerance is not contagious.
However, primary lactose intolerance, which results from the normal low-to-absent production of lactase enzyme in adulthood, is heritable. In other words, if neither of your parents has the mutation which lets their bodies produce lactase into adulthood, you aren’t likely to, either. Congenital lactose intolerance (the inability to digest lactose from birth) is also heritable, although extremely rare; it’s an autosomal-recessive disorder resulting from a different mutation in the LCT gene (the gene that allows the body to produce lactase).[1]