There's three ways you can download the styles:
1. Use the in-game Styles Manager (you'll need to enable Online Features in settings first). You can get to this via the settings menu; F3 on the title screen. If you've encountered a "missing styles" error during your current session, the relevant styles will be brought to the top of the list if they're available. Also - if Online Features is enabled, NL will directly prompt you to go to the Styles Manager every time a missing style issue is encountered.
2. You can manually download any style at: https://www.neolemmix.com/styles/12.8/(style name here).zip
3. You can download all styles at once with this ZIP:
https://www.neolemmix.com/download.php?id=393 - note that while the all-styles download
is completely up-to-date at the moment,
in general it is possible that it might be up to a month out of date at any given time.
Styles are usually not included with packs because the vast majority of styles are used by multiple packs, and it would inflate the download size (as well as create confusion around which pack has the most up-to-date version of the style) if packs always included them. They're not included in the main NL download (outside of the official L1 / ONML ones) because this would hugely inflate the filesize - while 60MB total isn't
too big a deal for downloading these days, several users have also reported that on weaker PCs the all-styles ZIP takes a very long time to extract.