Is the word лицеприятие understood by (the vast majority of) Russians?
I doubt that. Unless they have a dictionary to look it up. Unpopular since the second half of 19 century, the word has virtually fallen into disuse somewhere after 1930-1940.
Check it up at Russian National Corpus : we are talking about 1 instance of the word in 10 000 000, and even that one would likely be a stylization or quotation. Judging by mere frequency of use, it probably started to fall from active use as early as in 1870's: less than 1 instance per million is generally not a good frequency to have for an active word (the word is beyond 40-50 thousands most useful words you know).
"нелицеприятный" was more popular even then. And this is exactly why it has lost its original meaning in everyday speech: surely, you can look in the dictionary where it says that the word may mean "not based on personal predilection" — but its (unfrequent) modern use is mostly "a turgid way to say unpleasant in speech".
I have read about "нелицеприятный" a few years ago, so I made a good guess as to what "лицеприятие" means. Still, had to check the dictionary to be sure. You see, the word is not used anywhere in modern language aside from very specific sources. Unless you read such works, it is almost impossible for you to even encounter it. When reading 19 century literature you mostly guess the meaning from context and move on. It appears twice in "Anna Karenina" yet I probably didn't pay attention to memorize it from the book.