I feel I shouldn't be posting on this forum because I'm not sure if I fit the catagory. Yep, some of the time I'm a lone parent - round about 50% of the time - but on, near, alternate days I'm a single guy, sperated, a parent but my progeny are at their mums.
I always think of Lone Parent as being a parent who is no longer in a relationship with the other parent.
I am a LP because I have separated from my XH and I am the main caregiver for my DCs 6 days a week.
He is a LP in the practical sense once a week when they stay with him, but if he sees himself as a LP and faces the same issues as other single parents even when the DCs are not with him, then I wouldn't disagree.
I do have a second adult around a lot of the time as I have a DP (to whom I refer as 'partner', because I am too old to have a boyfriend, even though he doesn't live here!)
I am also a step-parent of sorts, as my DP has 2 DCs (they all stay with me sometimes, but DP takes no real parental responsibility for my DCs, but my DD refers to him as her SD and calls his DDs her sisters!)
Its all very confusing, but basically, if the caps fits, then you are a LP.