I have heard from various sources that say the hindu god Shiva is equated with Lucifer of the Christian and other faiths. Is this true?
No, I would not say that Shiva could be equated with Lucifer from the Christian (or other) teachings.
In the Hindu tradition, Shiva is simply one aspect of God, the other two being Brahma (the creator) and Vishnu (the sustainer). Shiva is the destroyer.
All three simply reflect the way things are in the universe around us.
Everything, including people, are created, maintained for a while, and then dissolved into something else. A major law of life is that everything is always changing. No need to make Shiva into a feared image or to equate this image to something diabolical.
Shiva can be well thought of as the “destroyer of our delusions,” something which is very needed on the spiritual path.
If you would like to learn more about the very deep spiritual implications of Shiva and others of the Hindu deities, please read the fascinating book by Swami Kriyananda called The Hindu Way of Awakening.
Lucifer represents a pull within us, away from the light of our own divine nature into the darkness of delusion. To read more about Lucifer, please see Steps 12 and 13 of The Art and Science of Raja Yoga.