Quick Overview: Overo Lethal White is caused by the overo gene when there are two copies of the gene present in the horse's genotype (the actual genes that are in the horse. The phenotype is what you see from the outside.) It is autosomal recessive, which means that it is a mutation on a non-sex chromosome and that the horse will only be affected by the disorder if both copies of the overo gene are present.
There is fairly strong evidence that all true overos are carriers of the mutation, but it is not know for certain at this time. The OLWS mutation is mainly found in frame overos, but it has been found in other overo patterned horses, and even solid colored paint horses that have ancestors with overo patterning. However, not all frame overos are carriers. (genetics can be so tricky) Personally I think that if you have a paint horse that you are going to breed, you should have it tested for OLWS. It costs only $25 at UC Davis in California, and is quick and easy to do. https://www.vgl.ucdavis.edu/services/horse.php
"Lethal White" or Dominant Lethal White is caused by the dominant white gene, so it is different from Overo Lethal White. I do not know much about it other than that it is typically caused by both copies of the dominant white gene being present. Just as a side note, cremello and perlino are caused by a double dose of one of the dilution genes, so they are not true whites and their genotype for the dominant white gene is ww (homozygous recessive). Post if you would like the sources for this stuff. I have been doing a lot of research on genetic disorders lately and can list sources etc. if you'd like. :)