If a brother puts a requirement on the nikkah paper that he wants his wife to never have been with a man before but she has repented from a past of close to zina actions, is she allowed to deny this with the intention of "The one who repents from sin is like one who did not sin"? Or would it count as a lie?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

A woman is not required to inform her suitor of her past sins. Rather, it is impermissible for her to inform him of that, as it is obligatory on her to conceal her sins. It was narrated on the authority of Abu Hurayrah that the Prophet said: “All members of my Ummah (nation) will be forgiven except the Mujaahiroon (i.e. those who sin publicly or announce sins)…” [Al-Bukhari and Muslim]

Therefore, there is nothing wrong with resorting to Tawriyah (deliberate ambiguity; i.e. to say something which has more than one meaning and intend a meaning different from what the listener is likely to understand) in this case. Resorting to Tawriyah in this situation is permissible as long as it does not entail undermining the rights of the addressee. An-Nawawi said in his book Al-Athkaar about Tawriyah:

If it is needed to realize a Sharee‘ah-acceptable benefit that outweighs the concern of misleading the addressee, or if it fulfills a (legitimate) need that cannot be fulfilled except by lying, then there is nothing wrong with using Tawriyah as an acceptable alternative. However, if there is no benefit to be served and no need, it is disliked, yet it is not prohibited unless it leads to taking something wrongfully or withholding someone’s rights, in which case it becomes prohibited. This is the governing rule in this matter. [End of Quote]

Allah Knows best.