I personally do have access to LexisNexis but you should be able to do similar research without it. All Washington appellate case law from 1854 to present is
available online and the courts themselves provide a search engine. The hard part is knowing what to search for. If you want to find how courts have interpreted a statute, you can search for the statutory number, but for some extra fun, Washington has used several different compilations of statutes over the years, so you have to consult, e.g.,
this table to convert the numbers for older cases. Legal research is a fair amount of work. You're always going to end up reading a lot of cases that turn out to be irrelevant before finding one that is on point. So you should expect that in advance.
With landlord and tenant issues, not everything is explicitly written in the statutes, so it can be even harder to find what you want because there isn't necessarily a specific statutory reference that you can search for; instead, you basically have to know what kind of terms the court will use, which requires a general background knowledge of law. There's not really an easy solution to that, but as you learn more law, it becomes progressively easier to find what you want in general. You're probably not just going to be able to jump right in and find everything you want, but if you put your mind to it, you can learn these skills if you want to. I hope that is of some assistance.