Tamara Marie,
Are you talking about doing this on LDS.org or in the Gospel Library? Without knowing, we can't give you a specific answer. However, there are some parts of content which cannot currently be highlighted. This includes headings, lists (numbered or bulleted), and at least some quotes which are offset or indented from the normal text (e.g. like song lyrics or poems often appear in the midst of other printed text). This is a known issue and they are working to fix it, but there's a LOT of work to be done. Perhaps you could give us a specific example (chapter and quote or whatever that you're trying to highlight) and we can verify that this is the case. For example, on LDS.org, in the first chapter of the BOM institute *teacher's* manual:
https://www.lds.org/manual/book-of-morm ... 5?lang=eng
...I can highlight the in-line quote from Elder Bednar, but I cannot highlight the bullet lists, the bold section headings, nor the fancified quote with the graphical bar on the left side (slightly more than half way down the page).
And in the student manual, pretty much everything is bulleted, so it cannot be highlighted.
NOTE: Lesson manuals are probably the most fluid content from the church. (The scriptures don't change; magazine issues don't change; but lesson manuals come and go and content changes from year to year and I expect this to be more frequent as we get more digital.) Therefore, when I find a quote from a lesson manual that I want to highlight, I go to the source (e.g. conference issue, scripture, etc.) and highlight that instead. Of course, this technique doesn't work if the source isn't available online or in the Gospel Library, and it doesn't work if the whole reason for highlighting is to hold a reference for in-class discussion of the lesson. Still, it's the best I can offer.
For reference, at least some text in institute manuals can be highlighted on LDS.org and in the Android Gospel Library.
If none of that addresses your question, please provide more specifics.
FWIW,
Liz