No, Lucid dreaming is not Yoga Nidra. Yoga Nidra is something entirely different. Yoga Nidra, meaning Yogic sleep is a technique Yogis's use to achieve deep sleep states while staying fully awake. The method usually is divided into 3 stages:
1) Lying down in corpse pose in a dark or dimly lit room with eyes closed, then progressively relaxing every part of the body systematically. This is usually done by first relaxing the front right hand side of the body. Then doing the same on the front left hand side. Then doing the back of the body. This is usually done for 2-3 rounds before proceeding to the next step.
2) Then rhythmic breathing is done in different parts of the body(abdomen, chest, throat and nose) This is done for 2-3 rounds before proceeding to the next step.
3) Then visualization of random images is done rapidly, holding no image for more than 15 seconds. (This mimics the dream state)
Usually Yogic Nidra also uses a suggestion or affirmation which is repeated 3 times at the start of Yoga Nidra and then 3 times at the end. It is similar to a hypnotic suggestion and it is believed Yoga Nidra facilitates the internalization of the suggestion.
It is claimed that 1 hour of Yoga Nidra is equivalent to 3-4 hours of good sound sleep. The more one does Yoga Nidra, the less need is there for sleep. Yoga Nidra is basically a form of self-hypnosis.
Now Lucid dreaming. Lucid Dreaming refers to a state when one wakes up in a dream and realizes that they are dreaming. Thus a lucid dreamer can then consciously take control of their dream and visualize anything they want. This can prove to be a very useful technique navigate ones subconscious and unconscious mind and visualize situations, like troublesome situations. The modern techniques used to induce Lucid dreaming is basically a modern reworking of Dream Yoga, an ancient Tibetan Buddhist practice.