For anyone who doesn't mind using chemicals, there is a link to some research on the best ones for leaf streak on the AHS leaf streak page here, second link at the bottom:
http://www.daylilies.org/ahs_d...
To do this without chemicals (it also depends what you consider a chemical because some household products are also chemicals) there are several steps you can take but there's probably no way to get rid of it for good. It would help to know roughly where you are or at least what hardiness zone.
Since leaf streak is believed to need an entry into the plant, such as from pest damage or weather injuries then you could try and figure out what is letting it in. If you overhead water, do it in the morning so the leaves can dry quickly instead of staying wet all night. In new plantings try to space the plants wider for good air circulation. In other words do what you would do for any fungal disease of plants. If you are in a climate where the plants die back for winter, clean up the old foliage in fall is another recommendation.
Also consider that not everything that looks like leaf streak actually is leaf streak.
