Is there any prohibition or recommendation in halacha regarding signing an office space lease during the three weeks? If so, where?
I assume you ask because you know one should not purchase a new house during the three weeks. The rationale is that one should not say the blessing of she'hechiyanu during that period (for more details see e.g., here under She-hechiyanu).
Since signing an office lease is not a purchase, it doesn't require a She-hechiyanu, and therefore I do not see why it would be forbidden for at least three reasons
- it resembles a business transaction which is allowed (e.g., see here regarding buying an apartment as a financial investment)
- YUTorah (here, V.1.B) also quotes R Moshe Feinstein that one may buy a new car or truck for business as this would be included in the category of minimizing business transactions, which we are lenient with nowadays
- if delaying the signature would cost money, it turns the matter from a pleasurable activity to avoiding a loss which also makes it permitted (see e.g., end of here).
As always, please ask your rav before applying anything you read here in practice.