How to translate this part of Te lucis?

It sounds like you're asking about these two lines in particular?

Præsta, Pater piíssime,
Patríque compar Unice,

The words here are in a somewhat unusual order, to fit the meter and the rhyme. A more usual ordering would be something like:

Pater piisime, Unice-que compar Patri, præsta…

I would translate this as "o most pious Father, and o One like unto the Father, vouch for…"

Grammatically, note that pater and compar are both also vocative—for most words, the nominative and the vocative look identical. So Pater piisime is a single vocative phrase ("o most blessed Father"), and Unice compar is also a single vocative phrase ("o One, like unto"). Compar acts like par "equal", and usually goes with a noun in the dative (the thing being compared to): in this case, the Father.