What do you mean by "online application"? To me, "online application" means simply that the application gets some data or pages from some webservice or website, and so requires the Internet for use, as opposed to an "offline application", which is completely usable without an Internet application.
Worklight creates a "native application", which is installed on a device. This has nothing at all to do with whether the application is "online" or "offline". Worklight, (I gather from search - I don't use Worklight) is similar to Phonegap, etc. It packages-up some web pages with a native browser control into a native app.
Can you be more clear about just what you are trying to accomplish?
This doesn't seem to be at all relevant to jQuery Mobile, though. You should seek more general help that isn't about jQuery Mobile elsewhere, so that we can keep this forum on-topic.
That is a native application. If it also does not consult a website or webservice, then it is also an offline application (not online).
That is exactly what Worklight is for. You can create either online or offline native mobile applications using Worklight.
I'd suggest you consult the Worklight documentation for further information on how to proceed.
jQuery Mobile can be a part of this solution, but you will need to learn to use Worklight in order to do this. I doubt there is much Worklight experience on this forum (much more for PhoneGap, which is a similar solution), but this is not the place to discuss Worklight or Phonegap, unless there is some specific problem using jQuery Mobile in that environment.