Would it be possible to drive from the Lake District to the Highlands and Skye in the morning, and arrive in Edinburgh for accommodation in the evening ?

It's possible, as long as you don't intend to play.

In a hurry, I drove from Lake District to stay overnight in Fort William, then stayed overnight on Skye Island and drove to Edinburgh. After all, you have to play, not drive.

In fact, it's a big island, even if you just come for a visit, you will be in a hurry, and you won't be able to play well or rest well. I suggest staying for at least 1-2 nights. We drove from Penzance in the west of England all the way to Bicester and then to London, which was also nearly 600 miles. The Mercedes-Benz E-class car refueled for about 80 pounds on the road.

I left the lake district at around 12 o'clock at night and went to Skye, had a cup of tea, and then stayed in Edinburgh. I arrived in Edinburgh at around 1 o'clock at night. When I crossed the Edinburgh Bridge into the city, I was dazed and almost began to doubt my life.

Arrive and leave, the time should be enough

I drove from Sky Island to the Lake District. It took ten hours and covered a distance of 600 kilometers. For reference.