How can I recover apps from a lost iPhone?

don’t know if my old phone was backed up to iCloud

If you don't know if you were backing up, you probably were not doing this.

Log on to iCloud using your Apple ID and Password and check to see if a backup and backup date is there. Post back on your results.

If you were not backing up, you can still re-download any purchased apps from the App Store using the same Apple account used to purchase them.