Lee is Adam's Chinese-American servant, but he's really more of a super assistant who takes care of everything and offers sage advice whenever it's needed (and it is needed pretty frequently). We're counting Lee as a Trask, because he's a fixture of the household.
You might be thinking, "Isn't Oriental an outdated and kind of offensive term?" YES. "Then why does Lee keep using it to describe himself?"
Well, for starters, "Oriental" wasn't offensive back in the day.
But still, Lee is the quintessential Other, which is the idea of a person who is set in contrast to some sort of dominant norm. More often than not, this has to do with race, ethnicity, or religion. You know how most literature in Western civilization is about white men? And you know how you kind of notice when a character isn't white, and their non-whiteness becomes a huge deal, and very often becomes the only feature by which they are defined as a character? Yup—it's a really problematic practice. (If you want to know more, check out this cool guy named Edward Saïd.)
That said, Steinbeck isn't being naïve and racist here. He's using Lee as a character to expose the idea of the Other (or in this case, the Oriental, though they are synonymous here). Rather than having Lee just be the wise Chinese servant who occasionally quotes Confucius to help move the plot along, Lee is a complex character who engages in multicultural dialogue (he learns Hebrew, for goodness sake), whose origins call into question ideas of nationality and ethnicity (is Lee Chinese or American?), and who really struggles with his identity (as the novel progresses, he gets less ostensibly "Chinese" to those around him).
Lee walks the line between being Chinese and being American; in fact, the entire point of his character is to show how unstable these national identities are. Lee fools everyone at first by speaking in pidgin, and then we come to find out that Lee was actually born in the United States. Like he says to Irish-born Samuel at one point,
"And in a few years you can almost disappear; while I, who was born in Grass Valley, went to school and several years to the University of California, have no chance of mixing […] To the so-called whites I was still a Chinese, but an untrustworthy one; and at the same time my Chinese friends steered clear of me." (15.2.39-41)
Lee just can't win. You know that whole dream of the Great American Melting Pot? Yeah, apparently that only works if you can blend in with your skin color. Like Lee says, the problem is that people have preconceptions about how Chinese people act:
"You look at a man's eyes, you see that he expects pidgin and a shuffle, so you speak pidgin and shuffle." (15.2.48)
People call Lee names that have to do with his Chinese-ness all the time: to Kate he's the Chinaman, to the nurse he's a Chink, to Horace Quinn he's Ching Chong. Hasn't anyone heard of political correctness? Apparently not.