"I have a second pair of eyeglasses."
Translation:J'ai une deuxième paire de lunettes.
"J'ai une deuxième paire des lunettes" would be the translation for "I have a second pair of the glasses.
The construction "paire de lunettes" is a "noun of noun", where the second noun, without an article, gives further information on the first noun in terms of its quality, content, material or purpose.
In English, you can find the same construction, like "a glass of milk" = un verre de lait; but sometimes, the English construction will be different, as in "a travel agency" = une agence de voyage.