A true push cut happens when the knife is held at 90 degree angle to the material being cut AND no 'draw' is used to change what part of the edge is making contact in the cut. You can do that by either pulling/pushing the knife (sawing) or changing the angle of presentation to the cut. So if you were simply push cutting printer paper there would only be a very tiny section of edge doing the cutting. Cutting on a slice you can draw the entire edge along the cut and make contact with every inch of the blade during the stroke. This is how most people cut in general as there are few cutting chores that require a true push cut. Shaving is one of them, cutting wood is another and even this may have some degree of slice unintentionally or not.
I wouldn't say that you 'should' be using 10 DPS on LC200N as one, I despise that word and the judgement it casts upon others. That is where I would suggest starting as a point to experiment with as ultimately your cutting technique/skill will have just as much over an impact on how this holds up for you as the material you will be cutting. In general if you are not chopping then 10 DPS should hold up for most knives and cutting (assuming no chopping or batonning) but this only applies to the edge bevel itself. The type of steel and hardening may require that you use a micro-bevel, in addition to the 10 DPS bevel, at a much steeper angle in order to sufficiently strengthen the apex for more brittle steels such as high carbide steels, etc.
If you're only slicing then actually the coarsest edge you can get sharp is going to last the longest. The other fact to understand is that the lower edge angle will continue cutting the longest in general. You can take a very low carbide/soft steel and sharpen it in a way that it will outperform even the highest carbide/hardness steels on the market. This is done by lowering the edge angle sufficiently and increasing the coarseness of the apex finish Most people do not have a grasp of this concept and will purchase very high carbide steels and take them to a high polish at the apex, which will of course severely limit slicing aggression and edge retention. Which is a bit of a strange thing as HC steels are best suited to high angles/low grit apex.
If you're only push cutting then you'll want to have the sharpest use possible using the highest grit finish you can apply to the apex cleanly. This will allow less force applied to the apex in cutting and subsequently higher edge retention as it enters the material with less resistance.