What is the smallest pt size curved line that can print at 175LPI offset

What's the smallest point size I can specify for a curve to be printed on an offset press at 175 LPI screen without the curve looking like broken up dots?

This will be a solid black color and I want the finest line width in pts possible but not too fine that the line screen breaks it up into irregular dots...

How small can I go in pt size for the line width? .25, .2 ?

 

Not sure about width but if you could go higher on lpi (300 lpi is perfect) just for this color?

 

Thanks! I checked and I can get 200 LPI maximum.

I can't afford to add a plate for the linework. I only have the budget to print this job on a 4-color CMYK so this linework will be on the K plate where there is also halftone screening of other elements happening.

Want to get the linework as fine as possible without specifying it so thin that it breaks up when output to the plate.