I've been noticing huge lag spikes as well (July 1-4), sometimes as much as 5-8 seconds!
PvE. NA PC. Vvardenfell, and delves and public dungeons in other zones as well.
Once I went to attack an NPC and had time to swipe at him 6 times and nothing happened, didn't even flinch from the hits, weapon sheathed. By the time the NPC reacted, and took zero damage BTW, I had to restart my AoE DoT abilities because the time had expired.
One 5 sec. spike at the bank in Vivec city.