My understand, and it could be wrong since as I said I didn't go...

My understand, and it could be wrong since as I said I didn't go into the whole story behind LNGLF, is that in simple terms an organisation decided off their own back that US investors may be interested in investing in LNG.asx so they created LNGLF. LNGLF buys, sells, and holds LNG.asx shares and as such by buying LNGLF you in effect indirectly hold LNG.asx shares. However the details of that arrangement and the agreement that exists between LNGLF and it's shareholders isn't something I have any knowledge of.

As you say, in the case of LNGLY, the situation is simple. Owning LNGLY means you own ADR's which by definition gives you ownership of the underlying LNG.ASX shares and the right to convert your ADR's to LNG.ASX shares at any time.