I would also be interested in the comparison of Fuerte v. Lanzarote as I plan to go in May
Is there any flat water in Lanzarote (like a lagoon)?
I have been to Fuerte only. For beginners its not the ideal spot (lot of rocks and the flat water is relatively small and people like to try tricks and shoot pro videos there amidst the beginers but it can be done, for sure. I learnt kiteboarding there myself and dont regret it. If anything, it teaches you to be careful, control the kite and go upwind fast so you can return to the little sandy area
I think its a worse place for the instructurs as they are afraid about the gear
At Fuerte, I think Corralejo is the best place to stay as you get the Flag beach there (sandy beach with some rocks in the water, or on the beach with low tide, and with some chop, small waves and little current) and its a nice town with shops, restaurants and nightlife. A short ride to the west is El Cotillo, where you have some bays with flat water (you just have to watch the tide and wind direction, I think it doesnt always work). They can get crowded in summer but I hope there will be less ppl in the spring.
In south you also have the Sotavento, the windiest spot - we actually did not kite there as its off-shore and gusty and thus not ideal for beginners. But with high tide there is supposed to be a lagoon filling with water ideal for learning. The south seemed more touristic to me, European pensioners everywhere, with Corralejo being the town with a better vibe.