To lay on the line usually means to make effort to succeed, but with a great chance of experiencing a loss or damage. To take a risk, to put something at risk.
It also means to make something clear - by saying it clearly, firmly, frankly.
For instance: Okay, I have to lay it on the line: either start cleaning up after yourself, or get used to living alone!
Here, it's closer to ''but if I have to admit it...''.
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