The Lens of Truth can be skipped completely. In most spots you can simply get by through memorizing where invisible objects or false passages are located.
The Bottom of the Well and Shadow Temples rely heavily on the Lens of Truth. Check out their respective pages to see how to get through these dungeons.
The Treasure Box Shop minigame consists of picking between one of two chests that randomly contain either a key or a rupee reward, within a series of 5 rooms. The Lens of Truth allows you to peek into the contents of the chest, eliminating the random factor completely. Technically, you can complete the minigame without the Lens (at only a 1/32 chance), but in a speedrun this isn't practical.
See Crossing the Haunted Wasteland for more information.