Learn Romanian: Doamnelor și domnilor, o să obținem victoria! - Ladies and gentlemen, we are going to achieve victory!

You are right that -lor is the plural ending for the Genitive and Dative cases. However, in Romanian, the plural Vocative case (used when addressing a group of people directly) is exactly the same as the plural Genitive/Dative form. So doamnelor can mean "of the ladies", but here it simply means "Ladies!".

Does this mean both masculine and feminine nouns use the exact same -lor ending when addressing a group?

Yes! Doamnă (lady) is feminine and domn (gentleman) is masculine, but in the plural Vocative, all nouns regardless of their gender take the -lor suffix.

What tense is o să obținem?

This is the popular spoken future tense. It uses the fixed phrase o să (meaning "will" or "going to") followed by the present subjunctive form of the verb. Because obținem is the "we" form, the whole phrase means "we will achieve".

Why does the sentence use victoria instead of just the dictionary form victorie?

Victoria has the feminine definite article -a attached to the base word victorie. While in English we often just say "achieve victory" (without "the"), Romanian naturally prefers the definite form for this expression, literally translating to "achieve the victory".