According to Lenovo – ThinkVision 15.6 inch Portable Monitor - M15, this monitor has two USB-C ports. It accepts DisplayPort Alt Mode input, and can do pass-through charging (maximum power unspecified) of a laptop.
There do not appear to be any other video input ports. As far as I know, USB-C (DisplayPort) to (whatever) cables and adapters are unidirectional and only work when the USB-C end is plugged into the video source (computer).
Since your MacBook Air (13-inch, Early 2015) does not have a USB-C port, that implies that this portable monitor is not compatible with your computer. You either need a newer computer that does have USB-C (DisplayPort) output or a different portable monitor that has an input (e.g., DisplayPort, Mini DisplayPort, HDMI, mini HDMI) for which you can get an adapter.