So, while Laurelorn and the Library of Mournings is the topic of the moment, I thought I'd almost entirely baselessly speculate about it.
We've been told it's twice the age of the White Tower. There's a lot of swing room in that statement. The White Tower took a thousand years to build (mile-high magic towers do that), so it's sort of important whether Cadaeth is measuring from the beginning of the construction, or the end.
If it's the beginning, that puts it at being built in -3868IC, if my maths serves. This would imply it was built as part of the city to begin with, when the colony was founded. If this is the case, I suspect (and suspect only) that it'll be easier to access (note, easier. Not easy), because it'll have been built for use as a research library and is probably under the control of whoever actually runs the city.
If twice the age counts from the end of the construction of the Tower, that implies it was built in -1490IC. This would mean it was built just after the Asur left the Old World. In this case, I suspect it was built either for a specific project (for instance, developing those nifty trees they have), or as a repository for the books and such of those who fell during the War. Or maybe even as payment for the Grey Lords, who IIRC, protected the city during the War. That might mean access is given by another organization. One which wants extra control over the project which is why the Library is only available if the project works out of Laurelorn.
Obviously this is all speculation, but it's fun speculation.