How the GPL applies in a Web context is not clear to me, either. Despite being served in discrete chunks as a result of distinct HTTP network fetches, does copyright law consider the application as a whole one work? It's unclear to me and not well-defined by existing case law.
However, the operation of the LGPL (rather than the GPL) can remain happily agnostic to the outcome of this question, since its copyleft extends only to a library and not to a whole application that uses the library. If your application uses an LGPL library in a way that the application code merely "combines with" the library (rather than modifies the library directly), you need only abide by copyleft requirements for that library and not your whole app. (See the phrase "Combined Work" throughout the LGPLv3 to understand its definition and copyleft requirements.)
How distribution applies to the Web is usually quite simple: if something ends up in RAM or storage on a user's computer in any form, then it has been distributed to them. If a piece of code lives on your own server and is never transmitted to a user in any form, then it has not been distributed. The client-side code of your application is distributed; each component that is (L)GPL-licensed must be accompanied with source code or with prominent offers for source code (but obviously any components not covered by copyleft licenses need not satisfy those copyleft requirements). Your server-side code is not distributed and creates no copyleft obligations (unless you use code under the much-stronger AGPL.)