The verbs lie and lay confuse many people.
If you learn their definitions, it might help you keep them straight.
Lie means "to be or to stay at rest in a horizontal position," while lay means "to beat or strike down with force" or "to put or set down."
The past tense (or -ed form) of lie is lay, and the -ing form is lying.
In casual conversation, if you say I think I'll lay down, then that's fine with me, but if you want your writing to be correct, then put those little fingers on the computer keys and tap out I think I'll lie down.
The past tense (or -ed form) of lay is laid, and the -ing form is laying.
Example: Students, please lay your essay papers on the table. The students did as they were told yesterday and laid their essay papers on the table.
If your dog only responds to "lay down," then he doesn't know standard English usage. Please teach him to "lie down."
Infinities of love,
Source: Understanding English Grammar by Martha Kolln