I love the fact the chandrayaan uses earths gravity for most of its journey. This is simply amazing idea of saving energy and realying alot on maths. That's incredible achivement over thousands of kms.
Not to be a thorn in your excitement but gravity assist is a standard technique for more than 40 years in space exploration. Literally every spacecraft uses it in some way or the other.
Not to be a thorn in your excitement but as an expert in orbital mechanics (I have a certificate from University of Kerbin) there is absolutely no assist anywhere in this manouver. The pattern is just raising apogee of the orbit around Earth by performing prograde burn close to perigee.
The only reason this could have any mechanical advantage is due to Oberth effect if the engine was low thrust type. With low thrust it takes long time to perform the burn and so part of the burn would be performed away from perigee which makes it less efficient. Splitting it would allow them to overall perform it closer to perigee.
Other than that it has no advantage over straight burn (ie.
directly from LEO to Moon using Hohmann transfer), mechanically, but it could have other advantages. Making last burn shorter makes it likely more precise than single long burn. It also probably allowed them to perform some burns to test the craft before the most important one. There might be other reasons like testing communications equipment which might be difficult in LEO but they might not want to perform it before committing to insertion.
Right, didn't Beresheet just do basically exactly this orbital insertion pattern? And we have the Parker Probe which is shutting back and forth between the Sun and Venus to do gravity boosts in an even more dramatic way. Heck, both Voyagers did back in 1977 although those were very simple boosts compared to what we can do today.