My comments below are on the basis that the deceased was the sole owner of the property in question. If she was a joint owner with her husband, then he will be a trustee of land and have control of the property, rather than the trustees of his late wife’s estate (who will have no effective control over the property).
If the husband has a right of occupancy of the property, I do not see that the trustees can impose a lodger upon him.
I see no reason why trustees should not have in place reasonable access arrangements to check the condition of the property and to satisfy themselves that the life tenant is complying with his obligations - if for no other reason that when they renew the insurance, they give a warranty as to the condition of the property.
I anticipate that the trustees are also the remaindermen entitled upon the termination of the life interest. If independent trustees were acting in their stead, would not the remaindermen expect such trustees to make regular checks to be satisfied that the life tenant was compliant? I see no reason, other than the personal relationships, why trustees should not undertake regular inspections (perhaps every couple of years) to be satisfied that the property is being maintained in an appropriate condition, and that the life tenant has not allowed “unauthorised “ occupation by a third party.