I I tell my student to use "to lie" when "to sit" makes sense, and use "to lay" when "to set" makes sense in the sentence. then they have to figure out the tenses (lay is the past tense of "to lie" sigh) Most English (and I mean the vast majority) get it wrong. In German I use liegen/sitzen and legen/setzen.
"Laid" is the past tense of "to lay," and "lay" is the past tense of "to lie." You would use "lay" here because he was lying on the balcony, not laying something down onto the balcony. http://www.quickanddirtytips.com/education/grammar/lay-versus-lie?page=all
Yup. "He lay the book on the table" makes no sense whatsoever in either technically correct grammar or informal colloquial language. (Although, I suppose it could be the subjunctive mood answer to some sort of hypothetical question, but it still sounds incredibly awkward.)
It all just goes to show you that this is a "rule" of the language that native speakers don't even abide by anymore. And this isn't even to mention the past participle of lie (has LAIN), which is a word that I don't think I've ever heard spoken in my life by anyone anywhere except for some middle school language arts teachers.
They should really accept that as an alternate answer. Though it may be "technically" grammatically incorrect, the overwhelming majority of native English speakers don't differentiate between "lay" and "lie" in everyday speech, let alone their past tenses. This is almost as fussy and antiquated a grammatical rule as "whom".