Why is there liquid at the bottom of my lemon meringue pie?
Water seeping from meringue is practically always coming from the egg whites. There are a few standard things you can do to reduce it. 

First, do not overbeat. For some reason, recipes love to direct people to beat egg whites "to stiff peaks". These are almost never needed, and can easily lead to self-destructing foam (the proteins continue tightening after the beating, squeezing the water out and creating large, easily-collapsed bubbles). Go for soft peaks at most. I have found that using a high speed setting also helps, and beating per hand almost always leads to weeping, even if stopped early. 

Second, use cream of tartar to create a stabler meringue without too much beating. 

Third, the cornstarch isn't binding enough of the free water. If you whip less, you will have less free water, but if it is still not enough, you can use something more effective, e.g. xanthan. 

Look around the site for more advice against weeping meringue. Also look at the pictures in that answer - the meringue there is for macarons, which are very sensitive to the meringue quality.