This page explains how to find and climb Lake Tower in Hyrule.
How to Find Lake Tower
Look southeast from Great Plateau Tower to see Lake Tower. It's at the end of a bridge. Pin it with the Sheikah Scope so you can go to it more easily. You can see the pin in your minimap, so it's easy to go toward it.
If you are having trouble figuring out which tower it is, you might want to activate Dueling Peaks Tower before going to Lake Tower, so you get the map of the surrounding region. That way, you will see the dirt road on the map that goes east from Great Plateau. There is a crossroads where a path goes south from there. Follow that south path and you will go over the Bridge of Hylia, which leads directly to Lake Tower.
How to Climb Lake Tower
The path up to the tower is riddled with Bokoblins and Lizalfos, so you will need to have decent weapons and armor to be able to reach the base of the tower. You can also try to use stealth to avoid the enemies.
The tower itself has many platforms, so it's easy to climb.