I'd guess because he is culturally Chinese.
According to Wikia, Lie Ren is based on Hua Mulan, a historical Chinese person.
Ren alludes to Hua Mulan.
- Monty Oum stated that each member of JNPR alludes to someone who crossdressed in their story. Mulan had to disguise herself as a man to sneak into the Chinese army.
- Despite Monty stating that real-world countries don't exist in RWBY, Ren is still based on Chinese culture as his clothing is reminiscent of traditional Chinese clothing and his habit of resting a coffee mug on his palm instead of holding it by its handle, a style seen more often in Eastern cultures, as Eastern-style mugs have no handles.
According to Wikipedia on Chinese name, the name order is surname - given name.
Modern Chinese names consist of a surname [...] which comes first [...], followed by a personal name [...].
Also, Wikipedia on Given name states the different order between Western order and Eastern order.
The order given name – family name, commonly known as the Western order, is used throughout most European countries and in countries that have cultures predominantly influenced by Western Europe (North and South America, North, East, Central and West India, Australia, New Zealand and the Philippines).
The order family name – given name, commonly known as the Eastern order, is primarily used in East Asia (for example in China, Japan, Korea, Malaysian Chinese, Singapore, Taiwan and Vietnam), as well as in Southern and North-Eastern parts of India, but also in Hungary. [...].
So, if his name is written in first-last name order, it will be Ren Lie.
Unfortunately, it's not that simple, because a new question will arise:
Why is Yang Xiao Long's initial Y instead of X then?
Logically, I admit it's hard to counter this counter-argument. Its Wikia article also mentions a trivia on her name:
Despite having a Chinese name, Yang's given name and surname are inverted. "Yang" would be the surname and her given name would be "Xiao Long". Furthermore, Chinese surnames are usually only one character. This can be explained by Remnant not following real-world customs.
One can argue that because her family is not fully a Chinese family (hint: her mother), that her name might not be in the Eastern order, but instead follows the Western order.