Under the "fair use" doctrine of copyright law, you are allowed to use limited portions of copyrighted works if you use them for certain purposes. These purposes include commentary on copyrighted works. So your use of commentary on country music lyrics wold fall under the fair use doctrine, and you would be allowed to use "snippets" from the songs. The "fair use" doctrine is set forth in 17 U.S. Code Section 107.
Unfortunately, there is no set quantity or amount of lines you can lawfully use under the "fair use" doctrine. Instead each case is judged individually on its own facts. The statute above 17 U.S. Code Section 107 indicates that whether or not a particular use constitutes "fair use" depends on:
(1) the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes;
(2) the nature of the copyrighted work;
(3) the amount and substantiality of the portion used in relation to the copyrighted work as a whole; and
(4) the effect of the use upon the potential market for or value of the copyrighted work.
So unfortunately I would not be able to give you an exact number of lines you would be able to use and still be safe. But generally, I would say that you would be safe if you used a couple of lines from a particular song or just enough for you to make the particular commentary you want to make about that song. Using any more than what is necessary to make your commentary might be risky.
I hope this helps.