We're sorry about the trouble with Lightroom 4.3. Would you mind telling us which macOS version you're working on? Are you getting an error/prompt or does the app open up to a blank screen? Have you tried re-installing Lightroom to check if that helps? If not, please try that to check if it helps.
If you're using macOS Catalina or macOS Big Sur, please ensure that Lightroom has the necessary permissions on your Mac using the steps mentioned below:
1. Go to the System Preferences for your Mac, then Security and Privacy, then select the Privacy tab.
2. Then select Accessibility from the list to the left & check if Photoshop is added to the list with a check mark in front of it.
3. If Photoshop is not a part of the list, please add it by unlocking the window first using the lock at the bottom left, then clicking the + icon & navigating to the Applications folder.
4. Also, grant permissions to Photoshop under Full disk access located in the same list as Accessibility.
5. Once done, restart the Mac & check if it helps.
If the issue persists, try resetting the Preferences of Lightroom by launching the app while pressing & holding the Shift + Option keys.