So, for days I had been struggling with this very peculiar problem. On my PC, I had installed a Intel PRO/1000 Pt Dual Port Server Adapter which came with 802.3ad dynamic link aggregation (i.e. LACP) support but for some reason or another, I could only successfully enable static link aggregation with my Netgear GS110TP switch. FWIW, I had absolutely no issues setting up LACP with my Synology 1813+ NAS.
After lots of trial and error, the culprit turned out to be the Symantec Endpoint Protection software running on my PC. I had this module called Network Threat Protection running and it must have been filtering the necessary network control messages required to establish an LACP link with my switch.
After I disabled Network Threat Protection, setting up LACP worked as a charm. In addition, it also had the side-effect of tremendously improving my PC-to-NAS copy speeds! See previous post on this topic.