Yes, you can use it that way. Native speakers do use it. To lay (or pile) it on thick is an idiom meaning to exaggerate or overstate something usually in order to flatter or invoke generosity or to make an emotion or experience seem more important or serious than it actually is.

My first impression of this question was someone putting too much icing on a cake. I'm not sure if I've heard anyone say this phrase other than cases where there is something being poured or applied. For example: I want a lot of chocolate on my ice cream! Lay it on thick! Apart from this usage I would say it's not very common to hear it often than a few times a year.

Australian don't. Instead they say "she/he really bungs it on" which has the same meaning.

Lay it on thick means......to make a thing bigger or more important than real.

People use it often enough that pretty much all native-English speakers know what it means. When used as an idiom, that means to act or talk in such a way much more seriously that the situation calls for. "I found a gray hair! Woe is me! My life is over!" "Aren't you laying it on a bit thick?'