I made up this dialogue quip to keep them straight.

“Lay the object down now.”
“I laid the object down yesterday.”
“I have laid the object down every day.”
“Don’t lie.”
“I’m going to lie down now.”
“I lay down last night.”
“I have lain many times.”

Even though fictional stories are most often written in the past tense, the story is usually current action, being seen or experienced by characters. For example: She lay her head on his shoulder. She laid her head on his shoulder yesterday as well.