These statements can be reconciled if one assumes that Budicius' wife was another sister and Anna was a second wife to Lot, the first being the sister of Aurelius. That would make her step-mother to Gawain and Mordred and make them Arthur's step-nephews. Lot is called, "mature in age," by Geoffrey at his wedding to Anna and she scarcely out of childhood. This is, however, conjecture and still leave irreconcilable contradictions in the ages of Gawain and Budicius' son Hoel. Regardless, Geoffrey did not catch the conflicts he created.
Most of the romances do not recognize an Anna or any other sister to Arthur other than his half-sister Morgause, prior daughter of Ygerna and her first husband the Duke of Cornwall. It was under his guise that Uther seduced her, but Arthur is the only offspring of that union. The romance authors have Morgause marry Lot.