"Lunar New Year" vs "Chinese New Year"  

One has nothing to do with the other, though both are Chinese. The lunar year is a  ONE-YEAR calendar based on the 12 phases of the moon, therefore roughly on 354 days, while our calendar is based on the sun phases.  Chinese New Year is the equivalent of our 1 January. it is generally end of January (this year on the 22). It is the most festived day for Asians.

I would use which ever depending on who I am around out of respect to the culture. I don't personally celebrate either but if I were to talk about it with Vietnamese people or around them, I would use Lunar New Year. And not to be mean to the people of China but I think their government is an abusive pile of crap and I hope those people rise up. I have zero respect for that government system but I would be respectful of the people. 

I think that while the term "Lunar New Year" is more commonly used in the United States, it is important that we respect the wishes of those who do not want to use it. As such, I would support efforts to make sure that both terms are used, and that there is no bias or preference toward one or the other.

The Lunar New Year is celebrated in other Asian countries like Vietnam, Korea and Japan, while the Chinese New Year is celebrated in China, Taiwan, Hong Kong and Singapore.

I never understood the divide of this and ignorantly, I just assumed they were the same thing. I didn't realize this until I went to Vietnam that they were not the same. I have assumed Lunar New Year to be the default in most countries which is why I always refereed to it that way.

Again, both are completely different ; therefore, it is NOT a matter of using one rather than the other. You MUST use "Lunar year" when you speak about YEAR and "Chinese New Year" when you speak about the Asian NEW YEAR