I’ve had a good look at this. The cause of the behaviour you describe is that under some circumstances your plugin doesn’t load the “modern-events-calendar-lite” text domain. It instead loads a text domain called “mec”.
This means that automatic (or “just in time”) domain loading is invoked when translations are displayed from the “modern-events-calendar-lite” domain.
In the case of automatic loading, WordPress checks for installed (system) translations before calling any filterable functions. This means Loco translate can’t override the file that gets loaded. I will add this as a caveat in my FAQ on custom file loading.
It’s worth mentioning also that your plugin seems to display translations BEFORE it’s attempted to load any, so relying on auto-loading is probably a good idea. For that reason I recommend you simply leave your system file in place. If you’re worried about adding unnecessary overhead loading two files, then ensure the system file is empty.
I’m marking this as resolved as I believe I’ve found the reason for the error and provided the only solution I can, which is to leave both files in place.