Not bloody likely
The LF351 is only capable of swinging its output within the range (Vcc-3V) to (Vee+3V), meaning that if you operate it on a single 12V supply, its output will only be valid in the range from ~ 3V to 9V. You will need an amplifier whose output swing includes ground, like an LM324 or LM358.
Why do you need 12V to the LM3916? It can be configured to progressively turn on the LEDs as the input signal goes from 0-1.25V. Also be aware that you cannot just amplify an audio (AC) signal and apply it to LM3914. You have to "rectify" the audio to turn it into a filtered slowly-varying signal proportional to the "average" or "peak" audio level before applying it to the 3916. Read the Typical Applications section of the LM3914 Data Sheet.