"The Libyans have admitted to this bombing." They never have done exactly that - they just gave into demands to pay damages - as part of the deal PMB referred to, as a price for getting back into the good books of the USA and its satellites, and escaping sanctions.

"On August 15, 2003, Libya's UN ambassador, Ahmed Own, submitted a letter to the UN Security Council formally accepting "responsibility for the actions of its officials" in relation to the Lockerbie bombing.[28] The Libyan government then proceeded to pay compensation to each family of US$8 million (from which legal fees of about US$2.5 million were deducted) and, as a result, the UN cancelled the sanctions that had been suspended four years earlier, and U.S. trade sanctions were lifted... On February 24, 2004, Libyan Prime Minister Shukri Ghanem stated in a BBC Radio 4 interview that his country had paid the compensation as the "price for peace" and to secure the lifting of sanctions. Asked if Libya did not accept guilt, he said, "I agree with that..."(From here)

In other words they accepted responsibility for whatever their officials had done - but they never said that that included bombing the aeroplane. And have continued to deny that there was any such involvement.

And they handed their man al-Megrahi over for trial - but that was was supposed to be a fair trial. In fact it appears likely that the judges convicted him against the weight of the evidence.