I think you're overstating the similarity a bit. The bible verse doesn't actually connect the festivity with the right hand and mourning with the left. They're separate verses. They're also not juxtaposed. Both those verses are from Ecclesiastes, but they're a few chapters apart. The bit about hearts of wise people in the house of mourning has nothing to do with right/left hands.

hi! if /u/itsallfolklore doesn't drop by to address this question in person, you may be interested in what he had to say last week on a similar topic:

How was the concept of clockwise/counterclockwise expressed before clocks or in societies where they weren't common?

I see that /u/gingerkid1234 has already provided an answer from the bible side. Let me try and give you some additional context from the Daodejing. It looks to me like you're referring to section 31 of the received text of the Daodejing - "吉事尚左，凶事尚右." When translating that, you don't really have to add the word "hand" if you don't want to. Anyway, this sentence comes from a passage about warfare, and how a sagely leader ought to act in such an instance. Here's the whole passage translated by D.C. Lau:

"It is because arms are instruments of ill omen and there are Things that detest them that one who has the way (Dao) does not abide by their use. The gentleman gives precedence to the left when at home, but to the right when he goes to war. Arms are instruments of ill omen, not the instruments of the gentleman. When one is compelled to use them, it is best to do so without relish. There is no glory in victory, and to glorify it despite this is to exult in the killing of men. One who exults in the killing of men will never have his way in the empire. On occasions of rejoicing precedence is given to the left; on occasions of mourning precedence is given to the right. A lieutenant's place is on the left; the general's place is on the right. This means that it is mourning rites that are observed. When great numbers of people are killed, one should weep over them with sorrow. When victorious in war, one should observe the rites of mourning."

This passage is a real mess - there are scholars who think that it is in need of re-arrangement, scholars who think that parts of this are actually bits of Wang Bi's commentary that got mixed in, scholars who think that this chapter may not be "authentic"... it's tricky to interpret as a result. But based on what /u/gingerkid1234 has said about the bible verses, I think it's safe to say that these two parts of these two texts are talking about quite different things.