There are no log retention settings (yet).
By default, once the log DB reaches 90%, the older logs get overwritten.
So depending on the amount of logs you're receiving on LEM, it could be anywhere from few weeks to over a year.
I believe LEM could improve the retention capabilities, by having some sort of categorization inside the Policy settings area.
I know we can select whether we want to keep them in log DB or not, but an additional setting to allow for log prioritization.retention could be useful.
E.g. the Threat events to be retained forever, while events with low value (system noise) could be set to be cleared in xx amount of time
As Valkos states, there's no way to hard code log retention in the LEM at the moment. Instead it's based on how much HDD space you have. You can use the Database Maintenance Report to tell how much data you're storing (and calculated in Days):
To increase retention you need to allocate additional HDD space: