I agree, if you just started, you'll get little aches for a little while (you didn't mention how long you've started cycling your road bike).

Get fit is one thing, but even if that's great, you'll need to look into cycling stretch exercises. I really wrecked my back two years ago because I didn't do any stretches pre and post. Got some ART done, and since then I've been stretching my back pre and post rides. You can do a search and find stretches specifically for cyclists with Lower back issues.