Lanzarote: Various routes between; San Bartolomé - Timanfaya National Park - La Santa - Valle de Malpaso Haria and Valle de Malpaso Haria.
Fuerteventura: La Oliva, Parque Natural Corralejo, Rural Park Betancuria and in the south, Janda Natural Park.
Lanzarote: There are just always good roads and beautiful landscapes. Sometimes there are holes in the streets, I recommend slightly wider tires, e.g. 28 inches. There are many road cyclists on the way.
Fuerteventura: There are always good roads. I recommend the region "Rural Park Betancuria", it is an amazing area, beautiful hills and landscape. Further south, there is a lot of traffic, especially on the beach road from Tarajalejo - Costa Calma - and also before Moro Jable! Ride through Costa Calma quickly, ...lots of tourism. 15km further from Costa Calma (before Morro Jable) there is still a lot of traffic. Therefore I rode in the direction of "La Pared", it was a very good idea, beautiful landscape, very dry and little traffic.
Note: There are many possibilities to rent racing bikes! The costs are around 120 euros per week for a very good racing bike (value, approx. 5'000 euros)!