I have an EAGLE project that uses some custom library components. If I transfer the .brd and .sch to other people, do I also need to include the .lbr files for them to be able to properly view my design?
The parts you used are embedded in the board and schematic files. In fact, the other people could recreate libraries which include all the parts on the board from just those two files with the exp-lbrs user language program (ULP).
They can makes changes to components, that's what the exp-lbrs ULP is used for. From the description of exp-lbrs.ulp
Export of libraries from a drawing.
This can be used to make individual changes to components in a project. Just load schematic, board or both, use this ULP to generate one or several libraries containing the used components. Make your changes in the library/libraries and use the UPDATE command to introduce the changes to schematic and/or board.