OpenType

I'd create a test document in Pages, then import to iBooks Author, noting any import errors/font subtitutions. Test on iPad to confirm.

Good luck in any case.

Do you already have the fonts from that company? You cannot install additional fonts on the iPad, so it does not make much sense to test using those. The question is whether you can display the characters you need properly with the fonts which the iPad already has. You may as well test directly in iB Author, which is free. Here is a list of the fonts:

http://support.apple.com/kb/HT4980

I would copy/paste a sample text with all the accented characters you need into iB Author and then switch among the fonts present in the iPad to see how it looks.

It is possible that both the keyboard layouts on the page you reference may work. The US Extended layout provided with OS X creates diacritics via both dead key and the "OT" method, and that should also be useable for Lakota. There is a chart here

http://homepage.mac.com/thgewecke/diacritics.html

I may give it try myself later, let us know how any tests you run come out. If you have a sample text as mentioned above, email me a copy (tom at bluesky dot org).

PS Could you indicate which of the various orthograhies mentioned here you are planning to use?

http://www.languagegeek.com/siouan/lakota.html

PSS If it turns out that only those custom fonts provide the quality of display you want, you could publish as a PDF instead of .ibooks format.