How can I back up my lost iPhone 12 Pro Max

You are not going to be able to backup your iPhone because you do not have it in your possession to back it up on a computer. Do you use iCloud for backups on that iPhone? If you do then you have a backup on iCloud. If you did not backup the iPhone or did not use iCloud for backups, then you do not have a backup and cannot create a backup now.

Axel F.

Backups MUST occur before something bad happens. If you didn't use the tools available to you to backup your iPhone, it's too late now.

Unfortunately, you cannot back up something that you do not have. And with no backup, you will have nothing to restore to the new replacement phone that you have now or will have soon.

I suggest that you make it a priority to set up automatic daily backups on your new phone.

You can’t

If you didn’t do any backups prior to loss then unfortunately you can’t retrieve the data on it.

Have you tried find my iPhone?