Actually, their purpose and the rationale of their designation is known; When Fisher returned to the Admiralty in 1915, he wanted more ships with 15 inch guns ordered, and in particular, more battlecruisers. This resulted in two of the Revenge class battleships being reordered as Battlecruisers (Renown and Repulse), but he did not have authorization from Parliment to order any further capital ships (as it was assumed the war would be over long before they'd be completed). He exploited a loophole that allowed him to order more Light Cruisers, hence the "Large Light Cruiser" designation.
The rationale for their design was to support an amphibious assault from the Baltic Sea (A pet project of Fisher's that never came to fruition), which required ships of a shallow draft to support the landings with heavy gunfire. Of course, the design compromises to achieve the shallow draft, high speed, and large guns were so extreme that the ships were tactically rather useless when completed, being built so lightly that they suffered damage from encountering bad weather and firing their own guns.
I used "All the World's Battleships from 1906 to Present"by Ian Sturton as a basis.
I'll quote from the Couragous section:
"To get around the Cabinet ruling against new capital ships Fisher ordered early in 1915 three 'large light cruisers' which were in fact light battlecruisers intended to support his proposed baltic landing.
The precise role, like everything else connected with Fisher's Baltic Plans, was never worked out, but it can be assumed that they were to provide gunfire support with their heavy guns and possibly to lure away German forces.
To that end their high speed and shallow draught made sense, but as with the original battlecruisers, the result was a very expensive solution to the problem."
So I am aware that they were intended for the Baltic operations but appearently it is not documented anywhere what their precise job in that operation was to be.
Anything else is speculation unless new documents have turned up where their actual mission profile is explained.