Is it normal for your lip piercing to bleed heavy hours after getting it?

Were you playing with it? You might have irritated it and opened the wound pretty badly, causing it to bleed heavily, either that, or they used a piercing needle gauge fairly too large for your lip piercing. I've experience piercing people with a piercing needle that's 2 gauges bigger, (For example, a lip piercing is 16g, I've pierce it with a 12gauge once) and it didn't bleed too bad, it bled for about 5-10 minutes.

It shouldnt be bleeding heavily at all. Especially not for hours after getting it pierced. Go see a doctor as soon as possible before you lose too much blood