They can run directly from an audio signal, usually via a 3.6K resistor. This is exactly how VU meters were originally intended to be used.. However, because of the diode bridge inside them, they can add distortion to the signal. How much distortion depends on the output impedance of the amplifier they are connected to. A little while go I did some tests on theEZTubeMixer transformer balanced outputs which have an output impedance of about 150 ohms. At 0VU, the distortion added by the VU meter is far in excess of the the distortion produced by the amplifier. Modern op amps have very low output impedances so the amount of distortion produced could be very small. However, many op amp outputs have series padding resistors in their outputs, typically around 47 ohms so these will also see significant diatortion produced by a directly connected VU meter.
Bottom line, for minimum distortion use a buffer. At Neve, back in the 70s, we used a lot of VU meters connected directly across the outputs. When testing for distortion, the procedure always insisted any VU meters were switched away from the outout being tested.
Cheers
Ian