I'll give the standard answer most of the lawyers on this site will give to this question: don't try to figure this all out on your own, Roger. There isn't a "term" that magically prevents you from being diluted. Rather, it's careful drafting/negotiating of the company documents that will protect you.
To start with, in US jurisdictions there are no "shares" in an LLC. There are "member interests," which do not correspond to the rights typically associated with shares of stock in a corporation unless the membership agreement is drafted to reflect such rights. If indeed you are talking about a membership interest in an LLC, throwing in a corporate anti-dilution clause will be useless unless the membership agreement contemplates a similar scheme by creating phantom stock (which is unlikely).
The Brad Feld article jimg provided is terrific for understanding how anti-dilution clauses can be structured from an economic perspective in a typical venture-oriented corporate capital structure, but, again, that is useless in the context of an LLC. No one can provide an answer to your question on how it would work in an LLC with knowing a lot more (i.e., reviewing the actual membership documents).
On the "profitability" question: Whether an equity holder in an LLC or a corporation has information rights to things like financial statements is somewhat complex. From a basic corporate law perspective, equity holders usually do not have rights to that information. The company can grant a contractual right to the information, or depending on the nature of the sale of securities to a particular equity owner there could be a securities law obligation to provide that info. But generally speaking, no, a minority equity owner doesn't have a right to financial info about the company unless the company contractually agrees to provide it.
(This is not legal advice, and no attorney/client relationship is created between us)