No, the light output of a lamp is the same, you’ve just focused more of it in a particular direction. It’s the same reason flashlights have a cone shaped mirror around the bulb. If it were possible to double light output, then putting a lamp between two mirrors would make infinite light.
This reminds me of a great demonstration of how directional antennas focus radio waves in one direction: https://youtu.be/lslHtCUSfN4
A mirror and a perfectly white wall both reflect (nearly) all the light that hits them, the only difference is in which direction they reflect it. White walls will scatter the light that hits them.
You’re just changing the direction of that light with a mirror. Picture a light bulb vs a light bulb in a flashlight with that reflector dish behind it.
Walls also do this, but to a lesser extent. If your concern is wasting light then get a lamp with a reflective directional shade. You know, like the Pixar lamp.