As you have correctly indicated, (a)"lay" (having one's entire body resting on a surface) is in the simple past tense (lie-->lay--> lain) while (b) "lay" (depositing something on a surface) is in the simple present tense (lay--> laid --> laid). They happen to have the same spelling.
You can use "lay" in both present and past tense if you are using it as two different verbs (a) and (b) in a sentence.
Example: Last night, as I (a) lay on my couch in the dark, I could see the burglar trying (b)to lay his hands on my wallet.
As you can see, although I used to-infinitive in (b), the action of the burglar is still in the past because I used "Last night".
We cannot rely on the verb tense alone to determine if something happened in the past, is happening now or going to happen in the future. We need to look at the entire sentence for its overall meaning as well.
I hope this helps.