If you want alerts based on the output of a script, you'd likely want to setup an EventSource. Currently there's no API endpoint for just alerts.
That said, you can have your current scripts send their output to LogicMonitor via LM Logs, then create an alert condition on the log contents. I do this with many of the scripts I have written that manage LM. They do things like sync in devices from a SoR, sync users from a custom directory, etc. When they run, they have sdtout that would normally be displayed on the screen or written to a log file. I recently change that so that most of my scripts write to the LM Logs ingestion API endpoint with that content. Then i can see the log output of my scripts right within LM. I haven't done it yet, but it wouldn't be hard to setup an alert condition on specific log entries based on the words that would indicate an issue.