Catalyzes the attachment of L-alanine to tRNA(Ala) in a two-step reaction: L-alanine is first activated by ATP to form Ala-AMP and then transferred to the acceptor end of tRNA(Ala). AlaRS also incorrectly activates the sterically smaller amino acid glycine as well as the sterically larger amino acid L-serine; generates 2-fold more mischarged Gly than Ser. These mischarged amino acids occur because the of inherent physicochemical limitations on discrimination between closely related amino acids (Ala, Gly and Ser) in the charging step. In vitro, in presence of high levels of lactate, also acts as a protein lactyltransferase that mediates lactylation of lysine residues in a large number of eukaryotic targets, including p53