I didn't say anything about lying, it was an hypothetical question out of interest.
I did my research on the USCIS website and found out that the spouse is eligible for a derivative visa via form I-485. Let me rephrase my original question then:
If one of us receives the green card through DV and the other one is eligible for derivative visa - do both applications go simultaneously or does the one getting the green card need to complete the application process first?

