Hi Patrick and welcome to the forums (and by implication welcome to your girlfriend as well).
There are a few things to mention here I think. Several options for tossing lyrics and beats from two different tracks together:
1) Acappella’s over track B. If you have/find lyrics only bits, you can clearly play those over any other track’s instrumental part. Keeping an eye on musical key and tempo of course. Regular DJ software can accommodate that quite easily.
2) Mashups, this is where you merge two or more tracks together. This COULD be by using the vocal part of a track with the beat or break part of another. Mashup software can help you do this, it’s more of a preparation thing. Also regular DJ software can help you here. Especially since the EQ (frequency control) per channel allows you to “bring out” the vocal part of a track by turning down the low frequencies and perhaps even a bit of the highs (experimentation is key here).
3) Producing. This is more about creating tracks from scratch, where you create your own beats as well. Clearly you can take vocals and add those to the track. This would work best with compatible vocals. Here you’d need production software, the most well-known is Ableton Live.
The second part of the equation is ambition level. Does she just want to dabble in this at home at her leisure or does she ever want to do this stuff live in front of other people (if only the family at the next house or bbq party)?
The main site offers entry level courses to both disciplines. If it is more the DJ-ing side that appeals to her, then “How To Digital DJ Fast” is the best primer to get going on basic stuff.
For producers the “Producing For DJ’s” would be a good place to start.
Both come with a full money back guarantee. So should she pick one or the other and during/after the course she thinks that is not the right thing for her, she can apply for a no-questions-asked refund.
Hope that helps some.