In Lightroom, if you go into the maps view, you can search for the location there then drag & drop the photo from the lower image bar onto the map which then adds the GPS info. No copy-n-paste required!
Personally I use GPS4Cam Pro which is a 2 part system, there’s an app on the phone where you start a trip, at the end of the trip it shows a QR code that you photograph. When you put the images on the computer, there’s a Mac (and windows) app which scans you photos for the QR code, uses that to get the gpx trail and then updates the exif with GPS locations. You then import to LR after that. GPS4Cam has worked well for me and is still available however, it seems that the project isn’t being updated anymore. The dropbox function stopped working a while ago. I’m expecting that at some point it just won’t work anymore but I’m getting what use out if it I can while I can.
Another possibility is that LR does have some capacity for incorporating GPX trails. There are quite a few iPhone apps for recording GPX trails. In LR’s map module, on the lower toolbar there’s an icon that looks like a zig-zag line. Click that, load up your GPX trail, there’s a slider to manage offset if there’s a difference between GPX time and you cameras time. LR then uses the times in the gpx trail and times of your photos to figure out where each one was taken.