Lens design - max lpmm, monochromatic light How can I approach this task:
I need to design diffraction-limited lens for monochromatic light (~1nm line width, so I guess no need to correct chromatic aberrations), geometry aberrations are also irrelevant BUT maximal lpmm required over as wide as possible area (i.e. coma need to be corrected for example) and NA should be at least 0.3-0.5. 
How should I approach this task?
Is Zemax is state of art software for that kind of tasks? What kinds of lens designs should I start to look at?
Manufacturing is not a problem (provided that there are no aspherical elements).
 A: Lens design is an art as much as a science, and is heavily based on experience. To do this, you would need at least a graduate level background in optical design, and preferably also years of experience. If you have that, Zemax would be quite acceptable, although I personally use Code V. Either one should be more than adequate. Oslo would also work. Generally lens desingers prefer to use what they already know.
In terms of a starting direction, it is best to begin with some standard design that has specs as close as possible to your goal. Given that you are imaging between finite conjugates (I'm assuming this because you are doing lithography) you would likely use something symmetrical about the stop, like a double gauss lens. The double gauss includes some elements for chromatic correction, but you can remove those for simplicity. You may need to add more to improve your performance later on.
In general, a good desk reference for finding a starting design is "Practical Optical System Layout: And Use of Stock Lenses" or "Modern Lens Design: A Resource Manual" by Warren J. Smith.
Of course because you are designing lenses, I assume you already own "Modern Optical Engineering" by Warren J. Smith, because anybody who wants to do any optical design should already be comfortable with that book. If you don't, own it, you're not really an optical engineer :)
