Casetext does not list unreported cases by Westlaw or Lexis citations. Instead, unreported cases on Casetext are cited according to their docket number, per the Bluebook standard.

We recommend finding unreported cases on Casetext by typing in the case name (without the Westlaw or Lexis citation) into the search bar.

For example, if I wanted to find the unreported case, Gray v. Toyota Motor Sales, U.S.A., Inc., 10-CV-03081(JS)(ETB) (E.D.N.Y. Sep. 17, 2012), I would enter Gray v. Toyota Motor Sales into the search bar, as shown below. I would not enter the Westlaw citation associated with this case, which is 2012 WL 4174362.

When I start typing Gray v. Toyota Motor Sales into the keyword search bar, a link to that case auto-populates beneath the search bar. I can then click on the link that appears beneath the search bar to go directly to my case.

It is more difficult to find an unreported case on Casetext using only the Lexis or Westlaw citation, but it is usually still possible. To do so, type in the Lexis or Westlaw citation into the keyword search bar as a phrase (in quotes) and then run a search.

You will then be taken to a list of cases that cite to your unreported case by the Lexis or Westlaw citation. From those search results, you can then find your unreported report case.

For example, if the only information I had about an unreported case was that the Lexis citation is 2012 U.S. Dist. LEXIS 15992, I would enter "2012 U.S. Dist. LEXIS 15992" into the search bar and click on the magnifying glass icon:

I am then taken to the search results page, which shows me that the case of Kim v. General Motors, LLC, 99 F. Supp. 3d 1096 (C.D. Cal. 2015) cites to my unreported case by the Lexis citation:

If I then click on the link to Kim v. General Motors, LLC, I can see that it uses the Lexis citation of 2012 U.S. Dist. LEXIS 15992 to refer to Gray v. Toyota Motor Sales: 

Now that I know the name of my unreported case, I can just type Gray v. Toyota Motor Sales into the search bar to go directly to my unreported case, as shown above.
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If you run a search for the name of your unreported case in your jurisdiction, you will be taken to a list of all cases that mention that case name in your selected jurisdiction. 

Then, from the "search within results" bar that appears at the top of the search results page, search for Lexis or WL. You will then see a list of all cases that discuss the name of your unreported case, using the Lexis or Westlaw citation.

It depends on the rules of your court and jurisdiction, as well as the preferences of your judge. 

A number of federal district courts accept citations to unreported federal district court decisions without the Lexis or Westlaw citation, as long as the citation properly includes the case number and year, per the Bluebook standard, as shown on Casetext. Still other courts allow you to cite to unreported decisions without the Lexis or Westlaw citation, as long as you submit a copy of the unreported decision to the court. And finally, some courts do not allow any citations to unreported or unpublished decisions.

When in doubt, consult your local rules, your judge's standing order, or contact the clerk to find out your judge's requirements for citing to unreported decisions.