I have read the LGPL license but its so complicated that I couldn't figure out the answer for my questions.
I want to use a LGPL library in my project. No change will be done in the LGPL library. This project is a website application used by registered users. The registered users are not charged to use the website.
So my question is can I use the LGPL library for this scenario?
Firstly, you can definitely use the library. Whether you want to, is a separate question.
If you do not modify the source code, and do not statically link to the library, or rely on internal data structures of the library, then you do not have to distribute the source code of your application to anyone who gets the binaries from you, but you have to distribute the original source code of the library.
If you do modify the source code, but do not statically link to the library, or rely on internal data structures of the library, then you do not have to distribute the source code of your application to anyone who gets the binaries from you but you have to distribute the modified source code of the library.
If you statically link to the library, or rely on internal data structures of the library, then you have to distribute the source code of your application to anyone who gets the binaries from you, and you have to distribute the original (or modified, if applicable) source code of the library as well.
If you are not distributing the binaries, or you are okay with the above constraints, then you can happily use the library.
HTH.