I have made the following changes based upon your feed back. Please let me know if there are any further corrections to be made. All the corrections I have made have been bolded and I am unsure but I believe Erebi is the Vocative of Erebus and I believe I have the correct number for umbrarum and tenebrarum.
Aurora, domina lucis primae, domina mea; obsecro te.
Aurora, lady of first light, my lady; I implore you.
Apollo, domine solis, magister musicae, domine mi, obsecro te.
Apollo, lord of the sun, master of music, my lord; I implore you.
Vulcane, domine ignis, faber divine, domine mi; obsecro te.
Vulcan, lord of fire, divine smith, my lord; I implore you.
Hade, Dis Pater,invisitate, domine mi; obsecro te.
Hades, wealthy father, the unseen, my lord; I implore you.
Mercuri, pes celer, nunti divine, domine mi; obsecro te.
Mercury, swift foot, divine messenger, my lord; I implore you.
Erebi, Pater umbrarum, Domine tenebrarum; domine mi, obsecro te
Erebus, Father of the shadows, Lord of darkness; my lord, I implore you.
Hade, Dis Pater, Rex mortuorum, domine mi, obsecro te.
Hades, Wealthy Father, King of the dead; my lord, I implore you.