I've only found references to Luxembourgers in Meriden in one source: Nicholas Gonner's Luxembourgers in the New World. According to Gonner, there were 16 families in Meriden in 1889. Most were factory workers. The size of the population fluctuated as some families headed to the Midwest.
I have a sneaking suspicion that individual families may not even know they were from Luxembourg. Meriden had a strong German population. Some of these families may have intermarried and begun to consider themselves German.
Take a look at Gonner's suggested source, the 1880 census. If your family is listed as Luxembourger, you may fall in among Gonner's 16 families. There's something to research there... Your next stop should probably be the Meriden Historical Society.