Would moving trigger a capability assessment for someone in LCWRA

After quering being on basic support despite being in the ESA Support Group, I've since been moved into the UC LCWRA and had my payment award amended. I currently live alone following the death of my mother. Therefore I stated all that on my migration forms. My family and I are now contemplting selling the home I live in (belonged to my mother, but left to my sister in her will but I pay all the bills, its all in my name etc) and my moving in with my father, in the same town as the house needs a lot of work, I haven't the funds and honestly its just a lot of stress and I have no attachment really to the place.

If I were to inform them of my move, does that trigger a Work capability assessment, or be more likely to do so? I pay a peppercorn rent to my sister (£15) and don't get housing benefits or help with my council tax (apart from the general single occupant reduction applicable to anyone) from the DWP. the only benefit I recieve is the UC LCWRA payment so it shouldn't impact how much they'd be paying me. I just really don't need the stress of an assessment right now (do any of us ever need it??)