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.