Is it fine to have a transparent bucket of water for hydroponics with recirculating water? the roots of the plants are obscure, but not so sure about the container.
No, having any part of your hydroponic system transparent is not a good idea. Even though the unavoidable algae growth (they appear anywhere where's enough light and plenty of water) is not harmful to the lettuce you plan to grow (or any other vegetables for that matter) it will eventually clog your recirculating system and thus might cause your pump to run dry and thus get destroyed. Even translucent plastic provides enough light for the algae to grow, so if I were you I won't leave any part of the water system exposed.
The only worry would be the increased chance of algae growing inside the container. However, with the water circulating it should not be a problem; good question naruse and welcome.