I too have similar issues with my LG-D405n phone. This started happening about a month ago.
Google Play Services keeps accumulating internal storage data until there's no space left if left unattended - to the point where other apps used during that time will simply crash and experience issues (I have lost up to several days worth of chat history on Whatsapp because of it on occasion).
I have pinpointed the issue for me to GPS usage. I used to have GPS turned off at all times and I had no issues. At some point after about a week of that issue I tried finding what could cause the issue, and it looks like (I presume an update of) Google Play Services turned the GPS back on as a "default" setting or something.
Turning off GPS seems to stop the issues for me. Without it, the data stays around the same amount for at least a week (as I haven't tested it longer yet), but the moment GPS is turned on again the storage hogging starts all over and within 1 day my phone gives the "running out of disc space" notification again. This is on "high accuracy" mode, I haven't checked the other settings.
In the past ~2 weeks I've been using GPS a lot more actively, and the issues have been going on accordingly.
In an attempt to fix it, I have used the "clear all data" option on Google Play Services, I have cleared the cache, uninstalled updates (revert to factory version of Google Play Services, causing GPS no longer to function until you update that specific part - which in turn causes the issue to rise again), installed a GPS app to delete and re-download AGPS data (which did help with the accuracy of my GPS, but did nothing for the memory issues), all to no avail.
I'm at a loss at this point on what else to try.