The murder itself, I don't think would ever result in a military response - Libya's response to our response, with the embassy besieged in Tripoli and alleged Libya-made bombs going off in London, that might maybe if the government felt the embassy staff were at risk if they didn't do something. For that you need Thatcher to be in the country at the time and I'm guessing the response would be an implied threat, "look at these planes in Cyprus that can deploy quick and have bombs".
From there, have the situation get more tense, implied threat made by implied threat, and then when suspected Libyan bombs go off in the UK, we respond with limited air strikes. (Basically what the US did OTL but with less planes) Not much will change in this timeline after that but I bet you get a lot of conspiracy theories about how Special Branch Killed Fletcher To Give Thatcher A Reason For More War In Time For The Local Elections
