The loan is presumably not secured on the house, in which case the creditor cannot "make them sell the house" without first getting a CCJ. If this is got and your son defaults on the payments under it then Lloyds can go back to Court to get a charging order securing the debt on the house. Once they have that they can go back to Court again and ask for an order for sale, but it is by no means certain that the judge would grant this.
If Lloyds have rejected your son's payment offer he should try to get help from a free money advice service, such as CAB or CCCS (be careful - there is a rogue outfit also calling itself by these initials which is a fee charger). He needs to make sure Lloyds gets his income & expenditure statement in writing, with his payment offer and an explanation of why his circumstances have changed so that he can not afford the original payments. Also, freezing of interest & charges should be requested. He should make the offered payments (keeping evidence) whether Lloyds accept the offer or not.
If Lloyds issue a County Court claim the financial statement on the form must be completed in the time limit given, and the payment offer repeated. Hopefully, the Court will then issue a CCJ for the amount he has offered. If they issue one for a higher amount he can ask in writing for a redetermination with a hearing - which will be at his local Court. Provided he always pays the amount of the CCJ payments on time then Lloyds cannot go back to Court for a charging order.