iMessages lagging

Hi, ashvi32.

This wouldn't be normal or expected behavior. To begin, we'd make sure your software is fully up to date:

"Update your iPhone, iPad, or iPod touch wirelessly

1. Back up your device using iCloud or your computer.
2. Plug your device into power and connect to the internet with Wi-Fi.
3. Go to Settings > General, then tap Software Update.
4. If you see two software update options available, choose the one that you want to install.
5. 
6. 
   
7. Tap Install Now. If you see Download and Install instead, tap it to download the update, enter your passcode, then tap Install Now. If you don't know your passcode, learn what to do.

You might see that your device is up to date and that there's an upgrade available. For example, even if your device is up to date with the latest version of iOS 14, there might be an option to upgrade to iOS 15. You might want to upgrade iOS when you pair an accessory with iPhone."

Update your iPhone, iPad, or iPod touch - Apple Support

If you're already updated and are still experiencing this, you will want to reach out to Apple for further support: Apple Support

Cheers.