Catalysis of the cleavage of a carbon-oxygen bond in ulvan, a carbohydrate composed of a repeating structure of [->4)-beta-D-GlcA-(1,4)-alpha-L-Rha 3S-(1->4)-alpha-L-IdoA-(1->4)-alpha-L-Rha 3S-(1-]n. Continued digest of ulvan with an enzyme that can catalyze this reaction results in ulvanobiouronic acid A 3-sulfate [->4)-beta-D-GlcpA-(1->4)-alpha-L-Rhap 3-sulfate-(1-]n with 4-deoxy-L-threo-hex-4-enopyranosiduronic acid at the non-reducing end.