Most states' limited liability company statutes contain provisions authorizing indemnification and advancement of legal expenses incurred by managers, officers, and other controlling persons resulting from lawsuits against them in their capacity as such.  Generally, these provisions allow the LLC to reimburse (indemnify) these "covered persons" for any legal expenses, except where the court finds bad faith, gross negligence, or some other "bad act," and companies may go a step further and pay such expenses during the pending litigation (advancement), provided that if the covered person is found to have committed a "bad act," the advanced funds must be repaid.

Delaware in particular had had a long history of dealing with indemnification and advancement issues in both the corporate context and with respect to alternative entities like LLCs.  Courts in many other states, including New York, have dealt with the issue only seldomly.  At the New York Business Divorce blog, Peter Mahler posts about developing New York case law in this area.