LLP, Limited Liability Partnership: a partnership where a partner's liability for the debts of the partnership is limited except in the case of liability for acts of professional negligence or malpractice. In some states, LLPs may only be formed for purposes of practicing a licensed profession, typically attorneys, accountants and architects. This is often the only form of limited partnership allowed for law firms (as opposed to general partnerships).
Idaho "corporation", "incorporated", "company", "limited", or the abbreviation "corp.", "inc.", "co.", or "ltd.", or words or abbreviations of like import in another language; provided however, that if the word "company" or its abbreviation is used it shall not be immediately preceded by the word "and" or by an abbreviation of or symbol representing the word "and" § 30-1-401 Idaho Statutes
On the other hand, if you are not responsible for its tax, then you should declare the equipment in Part III of the Business Property Statement (Equipment belonging to others). Where equipment is declared in Part III of the Business Property Statement, the Assessor will also send a Notice to File to the person reported as the equipment's actual owner.