The fees for on-chain payments are independent of the payment amount, while the fees for off-chain payments are proportional to the amount sent. It is trivial to compute the amount at which it makes more sense to make an on-chain payment.
Parameters used to compute the following numbers:
- the weight of a 2 inputs, 2 outputs on-chain transaction using p2wpkh is 836 vbytes
- a route in the lightning network has roughly a median 1000ppm proportional fee