Lacquer started as a bug product. The shiny coating is named after lac, a resin that tiny insects leave on the twigs of trees in southern Asia.
Etymonline defines lac as a red resinous substance deposited on twigs by insects. Wikipedia names the most commonly cultivated species: Kerria lacca. Farmers tie egg-bearing sticks to host trees, and the young insects coat the branches in resin, which is scraped off as sticklac. India, Thailand and China are major producers today.
The word is very old. Etymonline traces lac to Sanskrit laksha, "red dye," through Prakrit lakkha, Hindi lakh, Persian lak and Arabic lakk. Lac was used to dye wool and silk in ancient India, according to Wikipedia. The Mahabharata even tells of a House of Lac, built to house the Pandavas so it could be burned with them inside.
Why laksha? Etymonline says the origin is uncertain. One suggestion is that it literally means "one hundred thousand," for the swarms of insects on each branch. Wikipedia states that explanation as fact, but Etymonline lists it alongside other proposals, including a root meaning "color, dye."
Lacquer took a detour through Portugal. Etymonline derives it from obsolete French lacre, a kind of sealing wax. The French came from Portuguese lacre, an unexplained variant of lacca, "resinous substance." That lacca came from the Arabic lakk, so the Portuguese form is one more link in the chain.
In English the meanings shifted with the uses. In the 1570s lacquer meant a dye obtained from lac. By the 1670s it meant a gold-colored solution of shellac, used as a varnish. The verb, to lacquer, is recorded in the 1680s.
The same insect gave English several more words. Lake, the deep red pigment, came in the 1610s from French laque, because that pigment was first made from lac. Shellac, recorded in 1713, is lac melted into thin plates, a translation of French laque en écailles, "lac in scales."
Lac is still in use. Wikipedia reports that it varnishes violins and that India Post still uses lac sealing wax, though it is being phased out.