If someone successfully interrupt a cast right before you get it off, you are still capable of casting from the same tree afterwards.
Example: You cast a holy light, then spam flash of light during the cast time of holy light. If you are successfully interrupted at the end of the holy light then you'll still be able to cast flash of light after.
Or if you're casting LHW while spamming riptide, and get kicked, riptide will go off.
You do not require lag for this.