I cannot reproduce any trouble using either a free or paid account... Have you tried restarting your device?
Using a free account that does not sync to Lightroom cloud storage, there is no Clear Cache function. I added hundreds of photos, and then deleted the photos (and also emptied the trash inside the Lightroom app), and in iOS Settings > General > iPhone Storage > Lightroom, I see Documents & Data goes back to the original low amount used.
Using a paid account, I similarly imported and then synced photos, and after photos finished syncing I was able to see and use the 'Clear Cache' funtion Lightroom Settings > Local Storage.
Can you write clear steps or share a video screen capture showing what actions you are trying, and what the issue looks like?
Also, please try doing a full Backup and Restore of your device (using iCloud or iTunes/Finder). I wonder if the Restore process might smooth out some corruption.