Generally speaking, an out of state LLC that is doing business in another state (and "doing business" is the critical test) will have to "qualify" to do business in that other state. This typically involves filing paperwork in the other state and paying a fee. It may also trigger unique filing requirements in that target state which applies to its domestic LLC's. For example, if an LLC is formed in NJ and the business operates in NY as well, it would be a wise idea to have that LLC qualified to do business in NY by filing the appropriate form with the NY Dept of State. However, that NJ LLC will also have to fulfill the NY "publication" requirement which applies to NY LLC's. This is an expensive proposition.
Also, when you qualify in another state, you will generally have to file tax paperwork with that state as well (meaning multiple tax filings). Finally, the reason for all of the above is that if you are really doing business in another state and fail to qualify, a lawsuit arising from that state can have dire consequences (the biggest being the possible loss of your personal assets).
I hope this helps.
Disclaimer: This answer is for informational purposes only and