We engaged, and the LPI was shot down in the first 30 seconds, but a few seconds after that, I managed to CD a mine from Skye, gaining us our first kill:
Sadly though, the Scimitar and Greyhound together on my damaged ship resulted in my having to eject a few minutes later, but I managed to damage both of them before I fell. I really need to stock more mine sin future, I keep running out.