What is the value of 1986 us quarter?
It's worth 25 cents.
I'm not entirely sure by what you mean with "lost quarter" but a 1986-D quarter is only worth face value in circulated condition, however, it is worth a premium over face value in uncirculated condition since little US Mint sets were sold that year. However, if your coin has even the slightest hint of wear or any scratches, nicks or dings, its just worth 25 cents.
By far, the most valuable quarter is the 1916 Standing Liberty Quarter Dollar - its value in good condition (G4) is: $3000. places the value of the 1916 Quarter at $3900 in G4 and $35,000 in MS66 (but look fast, it may be higher by the time I finish typing this). The first US quarter from 1796 is listed at $12,000 and $400,000 in those grades.
The Mint has never made gold quarters. If you have a gold quarter then it has been plated which destroys the numismatic value of the coin. Its value is 25 cents plus the value of the little bit of gold they used to plate it. Some chemicals can cause the quarter to turn different colors. This also does not enhance the value of the coin.