You did not actually state a question. If you are wondering whether your fiance's child support obligations could result in a lien against a home you both own, the answer is yes. His assets--which includes his interest in the house, if you both are owners--is subject to liens to satisfy debts and judgments.

Going forward, if your fiance has a substantial debt or obligation, it would be better to keep finances and assets separate, so your finances and assets are not impacted by his obligations.