Well, you have a brief, if only partial answer so far. Signing up for iTunes Match is one way but may not be worth it, depending upon how many songs we're talking about unless you want to use Match anyway. For a few years after going non-DRM you could pay a small fee per song to upgrade but that ended a few years ago. Now the only way to do it through Apple is if the music you bought is still available through the iTunes Store. Signing up for Match will automatically upgrade the songs for you to 256k DRM-free. If you only have 2 or 3 songs and are not otherwise interested in Match it probably isn't worth the $25 fee; if they are no longer in the Store it isn't worth it.
If you only have a few songs you might consider re-purchasing them through another online service. The only way to re-purchase them through Apple is to set up a new AppleID and account because otherwise Apple will tell you you can't buy them because you already own them. 😐
Keep in mind you can still burn your tracks to a standard audio CD. Keep in mind also you can rip standard audio CDs with iTunes. 😉 Of course you're starting out with a lower quality and you'll lose a bit more quality when you convert back into a lossy format, but if you're not picky and don't want to pay for a solution...