can we locate lost apple watch if the watch was battery low and turned off?

If the Apple Watch still has power, then

https://iCloud.com -> Find My iPhone

This will locate all registered devices that can send location information to Apple, and includes your Apple Watch.

Or via your iPhone -> Find My app (if you do not have the "Find My" app, then download it from the App Store (free).

Or via your iPhone -> Watch app.

• Pull down on the screen to show the "Search" box -> "find"
• Tap "Find my Apple Watch"
• Tap on the (i) icon (info icon)
• Tap on "Find My Apple Watch". A map will appear telling you where the iPhone thinks your Apple Watch is located ASSUMING your Apple Watch has power, or it has been less than 24 hours.

I have misplaced my iwatch. How do i locate it?

I need to take off my card off my watch

No.