Retired English Teacher
It doesn't have to be followed by "this time", no. The main thing you need to remember is simply that "Last time" does not mean "formerly" or "previously" in any context. It always refers to a specific time event or encounter in the past.
Last time I went to the supermarket, I bought apples = I bought apples on my most recent visit to the supermarket.
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.