Yes, sadly I can confirm that 'lasciati' has the connotation of "broken up."

I think that this is the most probable meaning in this question, but "lasciarsi" in italiano could have several meanings! for example:

with the meaning 'stop to hold' : "Si tenevano per mano, poi si sono lasciati" = "they were holding each other by the hand, then they have left each other";

with the meaning 'separete by sb' : "stavano viaggiando insieme, si sono lasciati 5 minuti fa" = "they were travelling toghether, they have left each other 5 minutes ago";

and Others meanings that don't fit in this sentence.

It's plural.

it'd be "MI sono lasciato"

Possibly just 'sono lasciati'? i.e. without the 'si', although i think 'sono partiti' might be more common if not more accurate

Except that the "si" implies that they did something to themselves or each other.