Translation:Quelle lettre ?
In my opinion, no. "Laquelle" is a pronoun, and you cannot place it just before the noun to which it refers; it would be same as saying "elle lettre", for example, instead of "la lettre" or "une lettre" or something. It's not here the point that you are asking about "the" letter, or "a" letter, but that you must place adjective "quelle" (and not a pronoun "laquelle") along with the noun itself. Pronoun literally stands in place of a noun, so it is wrong to put it just before the noun to which it refers.
The letter, which one?
Here's some context:
"Take the letter to the post box, dear," says Mother. There are twenty-odd letters sitting on the tabletop.
"The letter, which one?" I ask.
"La lettre, laquelle ?" would be what I am asking in French, and it makes perfect sense if you have context like the little story I made up there ^_^
hope this helped