Yes, a brown flower can be turned into a different colour. It is easier to turn a diploid brown into a different colour than it is to turn a tetraploid brown into a different colour. That is simply because there are fewer genetic combinations for diploids than there are for tetraploids.
Daylilies have at least four different types of pigments: chlorophyll - the green of the leaves; anthocyanins (flavonoids) - reds, purples, pinks, lavenders, creams; carotenoids - oranges and yellows; and naphthalenes - light yellows.
Brownish flower colours can be green with purple or yellow and orange with purple, usually when there are substantial amounts of the green, yellow or orange pigment.
One way to change the brown is to reduce the amount of yellow or orange pigment and that can be done by using light coloured parents - near-whites, very light pinks or very light lavenders.
Browns are often described as 'muddy' or 'dirty' - and a general idea is that one can reduce the 'mud' or 'dirt' by using a cultivar that will 'clarify' the colour. Clarifier cultivars are near-whites, etc.
One may change the brown by crossing it to very dark clear reds or purples. Some of the seedlings should be clear reds and purples if enough seedlings are grown.
Or one can cross the brown to yellow cultivars. Some of the seedlings should be clear yellows.
One can get some ideas about what to use as the other parent by looking at the flower colours of the parents that produced the brown seedling.
In all cases, one needs to grow substantial numbers of seedlings from each cross because the majority of the seedlings will probably not be what you are looking for. A geneticist would consider several hundred seedlings from one cross as a small number of offspring. In this case, I would suggest at least 100 seedlings.
It is possible that the seedling numbers can be reduced depending on the ancestry (parents, grandparents, great grandparents) of the brown seedling.
The usual description of brown flower colours is that it is produced by mixtures of carotenoids (yellows and oranges) with one of the anthocyanins (delphinidin - which is purple in daylilies). That means that crosses with brown should be able to produce yellows, oranges or purples more easily than they produce other colours.
Yes, there are colours that when crossed are unlikely to produce a clear colour. The traditional answer is that yellows crossed to reds or yellows crossed to purples produce muddy colours. There are some yellows and some oranges that can be crossed with some reds and some purples and they produce clear colours. To find those one would need to look through the AHS registration database at parentages. Pure reds crossed with yellows should produce clear colours but many red daylilies are not pure reds - they have some purple and that can cause muddy colours.