Pour the milk into a large pot and place it over a low heat. Allow the milk to heat slowly but thoroughly (around 5-10 minutes) until it reaches a simmering point. It should be just lightly bubbling away, with plenty of steam coming off the surface.
Add the lemon juice or vinegar and stir just to combine. The mixture should separate into curds and whey - white cottage cheese like solids and a lemon opaque liquid. If this doesn't happen, continue cooking the mixture (without stirring too much) until the mixture separates. Do the same if the liquid is milky and not opaque. When the mixture separates, take it off the heat and allow to sit for 10 minutes.
Pour the mixture (curds and whey) through a nut milk bag in a sieve. Gather up the bag and rinse the curds thoroughly. This will help eliminate some of the tang from the lemon juice or vinegar.
Gently but thoroughly squeeze the remaining liquid out of the paneer. It's easy to break a nut milk bag by squeezing too hard (speaking from experience) so go slowly.
Shape the paneer into a tight disk while still in the nut milk bag. Place it on a flat plate that you can easily pop something heavy on, to help press the paneer of the final liquid. I used my skillet and eventually put my Dutch oven on top too.
Press for 2-3 hours or up to overnight. When you remove the paneer from the nut milk bag it should be solid and relatively dry.
The paneer keeps well in the fridge for a week.