Hello, ArunM2380.
Thank you for posting in Apple Support Communities. We understand that you’re trying to use your new Lenovo display with your MacBook Air using your USB-C Digital AV Multiport Adapter, but the HDMI cable that came with the display isn’t working with your adapter. We’d like to see if we can help.
Are you using the multipart adapter like the one we have linked above? If so, does it have an HDMI port in the middle like this one? We’re asking because there are different types of multiport adapters.
If there isn’t an HDMI port in your adapter you may need to purchase another adapter. You might also check other types of connections. For example, according to the Lenovo support site, your display also supports VGA. If your adapter has a VGA port, you may be able to use this type of connection.
ThinkVision T24i-20 (61F7-MAR2-WW) Monitor - Overview - Lenovo Support US
Apple also has some great support articles for connecting external monitors:
Use external monitors with your Mac - Apple Support
Get help with video issues on external displays connected to your Mac - Apple Support
Warmest Regards.