Ingesting application logs

Yes, you can definitely do this. In fact, you can do this using the traditional EventSource route simply by having the EventSource configured to follow your application log and alert whenever specific conditions are met.

It would be to your advantage to look into getting those logs into LM through the LM Logs feature. There are quite a few ways you can get the logs into LM Logs: api endpoint, fluentd, syslog, windows event logs, kubernetes native logs, logstash. Once you do, you can specify log pipelines (simply gatherings of log events) against which one or more regex based alerts can be configured.