I can't seem to find a solution for this on Google.

In every other application and game I've tried, my Lenovo T500 laptop intercepts those volume buttons and changes the volume accordingly, and the focused program doesn't "see" it happening.

In Dosbox, however, the volume buttons get treated as some combination of alphanumeric keys, and the OS doesn't even notice or change the volume. So I'll be in, say, Might & Magic: Worlds of Xeen and press the Volume Down button, and instead of the volume changing, my party tries to kick a wall and they injure themselves!

Does anyone know a way to fix this?

You could see if you can change the control settings for the game to stop that. Hardware control buttons shouldn't even be considered as inputs though.

My laptop is a little unique actually in that I don't have any buttons for volume. Instead I have a super-imposed third set of keys. Next to my left ctrl button is a button labeled "Fn" which I guess is function, and is labeled in blue. That in combination with my f3-f8, f12, arrow keys and the top keys over my number pad, home, Pg Up, pg Dn, and End, all function to change the sound, brightness, wireless, sleep mode, mute, and play/stop/fast rewind/forward. If you've got a newer laptop you might see if you can assign some keys like that, or if they already exist.

Other than that I'm not sure what to tell you other than to check your game settings and alter the key inputs.