Ok, here we go:

Actually, you have two different verbs here:
1) to lie ("to lie [by itself]"), past tense: lay, past participle: lain, present participle: lying
2) to lay ("to make sth. lie"), past tense & past perfect: laid, present participle: laying

The difference is NOT that someone is "doing the laying down" vs. " putting something down" but:
1) someone or something is lying down (by itself) - eg: I'm lying in bed
2) someone lays something down (in order to make it lie) - eg: I'm laying the pencil on the table (The result is that the pencil then will be lying (NOT laying) on the table)

According to this, the forms are:

1) I lie (in bed) - I lay (in bed) - I've lain (in bed) - I was lying (in bed) - I'll lie (in bed) - I'll be lying (in bed)

1) He lies (in bed) - he lay (in bed) - he's lain (in bed) - he was lying (in bed) - he'll lie (in bed) - he'll be lying (in bed)

and

2) I lay (it down) - I laid (it down) - I've laid (it down) - I was laying (it down) - I'll lay (it down) - I'll be laying (it down)

2) He lays (it down) - he laid (it down) - he's laid (it down) - he was laying (it down) - he'll lay (it down) - he'll be laying (it down)



Ok?
Hope that helps