If I refer back to a cited source in the literature review while writing the discussion section, (undergrad dissertation) should I cite the author again or am I free to use the information that has already been cited?
Just cite the author again. It should be clear what your source is every time you use a source.
There is no one-size fits all situation, so for student work, you should always ask your teacher what is expected.
In general, in scholarly writing that is meant for scholars to read, whenever you don't cite a source, you are implying that the idea in that sentence or paragraph is your own original thought. This is why scholarly articles include so many citations, including repeat citations--they are delineating their own ideas from that of other authors.
However, most other kinds of writing (such as publications meant to be read by the general public) are not that strict, and in fact, often don't like excessive citations since it gets annoying to read.
For undergraduate student work, you can always play it safe by adding the extra citation when in doubt, but again, it's best to ask your teacher what they expect.