In civil aviation, there are two kinds of lease, dry- and wet-lease. When you only need the plane and have the crew to operate it, and you need the plane in your fleet for at least 1 year, you dry-lease. 2/3rd of IndiGo's fleet is dry-leased. The lessee gets to put his corporate identity on the plane and use his ICAO/IATA paperwork on those planes.
In a wet-lease, you either don't have the crew to operate the plane you're leasing, or you're leasing for too short a period of time (eg: SpiceJet wet-leasing Czech Travel Service planes during Dushera-Diwali peak months). Here, the lessor gives you the plane, a crew, and keeps his own corporate identity and paperwork for the plane.
For the shortest duration of hire (think one off flights), you charter.
In this context, I think we have sufficient crew, but need the wares. i.e., although we have 25 M777 pieces, we have crew for more, say 70 pieces, and maybe minimal field-training is needed to transplant surplus crews from other systems such as Bofors. So I think this will be a dry-lease, guaranteed by undelivered M777s. A wet-lease would put US boots on Indian soil, and create a geopolitical clusterfuck.