There are like felling thousands of websites and information about the sights on the island. I will only mention the most important ones here by name, which one should have seen, be it with a guided bus tour, rented motorbike/scooter or rental car.
All of these sights are signposted and you can easily navigate there with apps today. Entry tickets are required for the sights marked in red. Usually around 8-12 €, but you get discounts if you combine several.
The Fire Mountains Montaña del Fuego, Los Hervideros, Jameos del Aqua, Jardín de Cactus, Mirador del Río, Cueva de los Verdes, LagOmar, Fundacion César Manrique, Monumento y Museo de Campesino, El Lago Verde, Salinas de Janubio, La Geria bis wine region El Griffo, Teguise Sunday Market, Stratified City, La Graciosa
A word of advice: don't get involved with any private guides who want to show you these attractions. These are superficial and usually expensive tours.
The real soul
the island is inland. All of the Canary Islands were created by volcanic eruptions and have been repeatedly reshaped over the millennia. You could even walk to La Graciosa and Fuerteventura during the last Ice Age.
The Guanches were apparently the first indigenous people who migrated from North Africa around the 10th century. They actually had no idea about shipbuilding and therefore lived completely isolated. In the 15th century, more and more people from other regions settled the islands, brought diseases and enslaved many Guanches.
Between 1569 and 1749 there were many pirate attacks on Lanzarote, where many people were kidnapped or killed as slaves. Teguise was the capital until 1852 and was replaced by Arrecife because it was larger and also had better transport connections.
See Lanzarote with different eyes
Once you've seen the sights and artwork of César Manriques, you can lie down on the beaches and unwind.
But you can also look at Lanzarote from the original side. Then the brown-black suddenly turns into a colorful world of colors.
There is definitely one person I can highly recommend: This is Harry Graner, nicknamed "Mash". His website is called: Lanzarote Feeling. He leads hiking tours with Cordual Koch, some of them along under the island, you can visit the old paths of the Guanches, go swimming in the natural pools or just hike around volcanoes and have everything explained to you. You discover an unspeakable variety of colors that you will not see as a normal sightseeing tourist and if you do, then you don't know anything about it or overlook it.
Mash has walked the island since 1999 and still searches it today. He knows every path and every volcano. He also explains the flora, how and why it grows here and which volcano has special features, why there are so many colors and what their origins are. I don't know any other person who knows so much about the island, the plants and the volcanism.
I've done a few tours with him myself and can only say that finding out more and more about the secrets of the island with the two of them becomes addictive. I can warmly recommend Lanzarote feeling.