You can drive yourself to the neighboring island of Lazarotte. To do this, you need to buy a ferry ticket (preferably online) and go to the port of Corralejo:
https://goo.gl/maps/NuidH63syYi7LBT56
There are many websites that offer tickets - but remember you also need a car ticket!
The biggest attraction of this island is the Timanfaya National Park and self-guided tours are VERY limited there.
In our opinion, the most sensible thing to do is to take a coach trip - coaches can enter places where it is impossible to go even on foot.
Many travel agencies on the island offer such trips and it is worth choosing the one that takes the first ferry in the morning (those who sleep longer, then stand in lines for hours).
We ourselves used the Polish office of rico-canarias.pl
https://rico-canarias.pl/wycieczki/lanzarote/
but if you speak English, use other offers such as: