I belong to a lone parent group and had this discussion with them recently as I wanted clarification as to who the group was open too.
I gave the example of someone I know who has two children with her ex and a new baby with a new partner. Doesn't live with the new partner as such, he lives a couple of houses down the road and she see's him every day and are planning to move in together at some point once the join mortgage he has with his dad (who lives at same address) can be sorted out and his dad can move somewhere else.
For me she will always be lone parent to her older two, but I don't think of her as being a lone parent when it comes to her younger child. But they said she is a lone parent now, but once she moves in with new partner she will no longer be a lone parent to any of the children. They also said they considered her a lone parent to the youngest as she was not living with her partner even though she has all the support from him that a couple living together would have.
I said I didn't think that was how she saw the situation as dad saw his child daily, often they would stay at one or other house all together and she could rely on dad for financial support and to have child whenever she needed him too. They did family things together when he wasn't working at weekends etc, and child was only going to playschool 4 days out of 5 so dad could see more of her on his day off before she starts primary school. The reasons for remaining in separate houses was purely because of financial issues and they were expecting another baby in a couple of months time and planning a future together as a family.
So it is a tricky definition really. Their definition being someone who lives alone and only pays council tax for 1 person living at the residence. I don't entirely agree with it, but finding a better definition which fits most situations is not easy.
I do think there is a big difference between lone parents who are completely alone and get no breaks and their child never sees their other parent, and those who may be separated but children still have regular contact with the other parent (ie co-parenting but separated). Also family support can be invaluable and some parents who might be considered lone parents do not consider themselves as such because of the family support they have. It doesn't have to be the child's parent you live with to be a 'family' rather than a lone parent. It can be a new partner, other family members etc.
Like anything it is impossible to pigeon hole everyone by a simple definition. I consider myself a lone parent. I fall into the category that I live alone, get no support from my son's father, (he never sees him and never has), and get very little practicle help from anyone else. Every single decision, bill and arangement has to be made by myself. No-one else will pick up the pieces is I don't.
One of my biggest concerns at the moment is the fact I don't have a will. I know I should have one but I do not know who I would leave my ds to be cared for by if something happened to me. So that makes it tricky to sort out the details of a will! That brings it home for me just how alone I am.
Gilly