As the are selling their core asset they will (like you said)...

As the are selling their core asset they will (like you said) need a project?
I will assume that they are getting in principle advice from the ASX as well.

Further to that, my thoughts and opinions based on my interpretations and understanding of the ASX Listing rules..

Why are the payments for the remaining sale of Goulamina over 2 tranches?

This could be advantageous to Leo Lithium on the basis of applying to get re-admitted to quotation prior to the first tranche being paid as they will still be owners (albeit 40%) of the Goulamina project, deeming the first tranche payment only a partial divestment of its core asset?
There are percentage definitions of being a partial divestment, but I'll be buggered if I can find them.
~ this will allow them to continue as a going concern up until the full payment is received.
~ will management of the Goulamina project being handed over to Ganfeng June1 be a hurdle?

It may also allow it to meet the asset test (less than half of its total tangible assets is cash) for being re-admitted to quotation, the royalty stream (receivables) is not included in total tangible assets.
~ The asset test is a condition under Chapter 1 when applying for admittance to the ASX, but is it applicable in the case for being re-admitted?

It may also provide the time (June 2025) to find a project to JV, merge with a listed entity, backdoor list (unlisted entity wanting to list) or commit funds to a project build (converter).

++ Something like a JV with the likes of ERW (disclosure: not a shareholder) that have just tripped over a "large stacked pegmatite swarm" adjacent to SQM/Hancock (previous Azure) Andover project. SOI 96 million, cash at end of last quarter $3.4m, Heritage surveys yet to be conducted (these are proving to be problematic causing delays to exploration) __ LLL could provide cash via a joint venture to help fund drilling, consolation shares to LLL shareholders as part of the deal, ERW to provide the land (after sterilisation) to build a convertor right here in Australia with Ganfeng as per item 2 of the now cancelled Cooperation Agreement, and (convert spodumene) tolling agreement with SQM.

LLL can't be re-admitted if they have no core business (or what passes) as a core business, royalty stream and having cash won't be applicable as they are not (currently) a financial entity.

This is advantageous to Ganfeng;
(a) It allows the dust to settle on its working relationship with the GoV before handing over the 2nd trance payment
(b) Although (publicly at least) the LLL/Ganfeng relationship is still strong but the delayed (2nd tranche) payment does keep LLL management on the hook per se, so they don't just exit the building at years end if Ganfeng are still not competent in running the mine.
(c) LLL providing service to Ganfeng to build their Lithium mine capabilities is why they need LLL (or more specifically) LLL management expertise as the licence can't be transferred or Ganfeng can't be the operator of the mine until such time they are capable.

I can't see the company (nor do I want them to) be re-admitted any time soon.
Also in my opinion, winding the Company up quickly would be in ALL shareholders best interest.

cheers