My mom lock out her iPhone

You will need the Apple ID and password after restoring the phone in order to get past Activation Lock. Normally the Apple ID is your email address, so you or she should know that (just look at an email from her). If you don’t know the Apple ID password start here→If you forgot your Apple ID password - Apple Support

Once you have the Apple ID and password, If your device has iOS 15.2 or later installed, you can reset it without a computer; check out this link→How to reset your iPhone, iPad, or iPod touch when you forgot your passcode - Apple Support. Otherwise you will need a computer:

See this Apple support link→If you forgot the passcode on your iPhone, or your iPhone is disabled - Apple Support

Or watch this companion video ⬇️

After restoring the phone using one of the methods above you can restore your most recent backup.

Is she the original iPhone owner?

• Yes. If you forgot your Apple ID email address or phone number - Apple Support
• No. How to remove Activation Lock - Apple Support

In that case, see “Start a support request” in the Activation Lock article I linked above.