The phrase often implies a problem or unwanted task, suggesting it's not a welcome action. My coworker went on vacation and dumped all his work in my lap.
Pro Tip 2/3
Unexpected Responsibility
It's used when someone is given a task without prior warning or preparation. I was about to leave when my boss dropped the monthly report in my lap.
Pro Tip 3/3
Empathy in Usage
Be aware of the emotional burden; the phrase can convey frustration or annoyance. On her first day, they dropped the whole filing system in her lap.