Lambda made (and makes) excellent power supplies, so I see nothing wrong with starting with this power supply. Apart from obvious limitations like no computer control and only a single channel this power supply should perform very similar to new power supplies, and is better made than the cheap power supplies that go under various names often sold new on eBay. If you didn't get a manual, you can get a PDF copy at
ArtekManuals, but I don't really see a reason to need this manual unless you need to repair it or want to use the remote programming / sensing connections at the back.
According to Ohm's law, putting 20 V across a 1 kohm resistor would cause 20 ma current to flow. You don't mention the zener voltage, but from your description I assume it would be about 5V, so the same argument would still apply (15V across 1 kohm would mean 15 mA would flow, more than the 10 mA limit). Since you limit the current to 10 mA, the power supply will reduce the voltage to keep the current under 10 mA. Increase the current limit and you should see that the voltage remains stable under load.