I lost my iPhone in a lake. I cannot find it but it is still turned on. Is there a way to access the information on that phone so I can back it up remotely?

If it’s ‘in the lake’ ... it’s not going to be operating for very long. You can only use your last backup, which is done automatically every day on your iCloud backup. You can only hope that not much was added in just one day, since your last iCloud backup. When you get your new iPhone, you can restore from your last iCloud backup on your drowned iPhone.