Skill lag often happens in intense and large-scale battles. It’s simply too much tasks to process in too short time.
Eve Online had similar problems in huge spaceship battles, where actions were even delayed by 10 minutes plus.
Eve Online introduced the Time Dilation mechanic which simply slows down the time locally to process all actions in a timely manner.
A similar system could be introduced for large-scale fights which affects everyone within sight on the center of the battle: A Track of Time debuff (not cleansable) which variably slows down movement, dodging, projectiles, auto-attacks and any other non-instant action to reduce skill lag to a minimum; buffs and debuffs as well should tick slower while affected by Track of Time.
It can also be explained in terms of role-play: There’s so much going on at the same time that you try to be aware of everything around you, time feels ticking slower.