Lækjarkot is located 125 km. from Keflavik 1 hour 45 minutes on a regular day.
More detailed directions.
First of all you take the main road 41 from Keflavík Airport which leads you to Reykjavík. It's about 50km drive or 45 minutes. 
The distance from Reykjavík to Lækjarkot is 74 km. Estimated driving distance 60 minutes.
You take the nr.1 ring road northbound and drive on, through Hvalfjarðargöng tunnel and towards town called Borgarnes.  You will cross the long bridge just before you enter Borgarnes and continue to drive through the town by taking a right turn, following the nr. 1 ring road.  Lækjarkot is loctaed by the ring road on your left hand side about 6 km. further than Borgarnes. 

Here you can see a video of the property taken summer of 2016: