Peroxisomal 2-OH acyl-CoA lyase involved in the cleavage (C1 removal) reaction in the fatty acid alpha-oxydation in a thiamine pyrophosphate (TPP)-dependent manner. Involved in the degradation of 3-methyl-branched fatty acids and the shortening of 2-hydroxy long-chain fatty acids. a 2-hydroxy-3-methyl fatty acyl-CoA = a 2-methyl-branched fatty aldehyde + formyl-CoA an (R)-2-hydroxy-long-chain-fatty acyl-CoA = a long-chain fatty aldehyde + formyl-CoA 2-hydroxy-3-methylhexadecanoyl-CoA = 2-methylpentadecanal + formyl-CoA 2-hydroxyoctadecanoyl-CoA = formyl-CoA + heptadecanal Binds 1 Mg(2+) ion per subunit. Binds 1 thiamine pyrophosphate per subunit. Homotetramer. Belongs to the TPP enzyme family.