The Lanayru Tower is east of the Dueling Peaks region. If you are heading to the Zora's Domain to meet Divine Beast Vah Ruta, you will likely come by this Tower. The fastest way to get to it is by going north from Kakariko Village, following the cliff path east, and then Paragliding into the valley to cross the large river.
The Tower itself, however, is in the center of an infestation of enemies. There are Lizalfos and Wizzrobes everywhere which can make this a challenging Tower to clear. The best time to try this Tower is at night, as the Lizalfos are prone to sleeping. Take your time, abuse your Bombs, and save often.