As a pre-requisite, a LEI DOMAIN should only be registered when the applicant uses an FSA ACCREDITED registrar anywhere in the world. The registrar checks the applicant, and is supervised by the registry and Financial Services Authority.
The largest benefit would however accrue from the PUBLIC OVERSIGHT, since anybody being able to access the Internet can verify the LEI DOMAIN information and can raise a concern or objection of non-valid data to the registrar-registry. Information to be placed is template-like (see http://telnic.tel as example) and transparent due to the nature of the Internet.

LEI DOMAIN content (the necessary information the counterparty must provide) is accessible at no cost by all people being able to use the Internet ??? and multilateral synchronization issues are solved through the Domain Name System (DNS).
LEI DOMAIN information can be updated real time. If the Registrant or Registry ???pulls the plug??? on LEI DOMAINS, i.e., they are no longer valid counterparties ??? this action can be seen the very same moment it happens around the world. Uniqueness, neutrality, reliability, open source, and PUBLIC PROPAGATION AND VISIBILITY (transparency) are typical benefits of the DNS.
Which central system would allow this to happen at minimal cost for the involved?
As a new solution possible as of 2012, is to apply to ICANN to register .LEI as a Top Level Domain.

Epiphany!