A well production method uses side gas lift valves above a packer and an ESP below the packer. In a gas lift mode, a controller turns the ESP motor off, and shifts a tubing valve below the packer to a gas lift position while flowing gas down the casing. While in the gas lift mode, a pressure gauge monitors motor lubricant pressure, which correlates with a flowing bottom hole pressure of the well fluid in the lower casing annulus. In an ESP mode, the controller stops the flow of gas from the gas source, shifts the tubing valve to an ESP position and turns on the motor, causing well fluid to flow through the pump intake. The pressure gauge continues to monitor the lubricant pressure during the ESP mode.