"We have lived here since last summer."
Translation:Vi har bott här sedan förra sommaren.
No, sist means last out of a number, not ’previous’ as in this example. If you were talking about something that happened during three summers in the past, you could say sista sommaren to talk about the third one of those, because you have a number and you talk about the last. But if you mean last summer as in the summer that just was, you say förra.