Your question is a bit confusing because the word "duty" as it applies to the Lanham Act can only be read under the context of the owner of the mark doing something or proving its mark to be worthy in order to get it registered. Based on that, the answer to your question can be much more accurate.
The Lanham Act (2005), is in Title 15 of the U.S. Code, and it consists on all the statutes that protect trademarks at the federal level. A trademark is the only intellectual property that can be regulated both at the state and at the federal level, therefore, the Lanham may cite all that statutes, but it is by no means the only law that governs trademark law.
However, Lanham does regulate the use of trademarks in commerce. See 15 USC 1055, where the act is clear about what to do prior to using a mark.
If first use of a mark by a person is controlled by the registrant or applicant for registration of the mark with respect to the nature and quality of the goods or services, such first use shall inure to the benefit of the registrant or applicant, as the case may be.
Therefore, the principal registrant of the mark should be the first to benefit from the mark being used by others, according to the statute of this act. Moreover, the user of the mark must be aware of this and understand that it is the applicant of the mark that will benefit first from the first usage.
Now, if your question refers to what duties the Lanham Act requires they are the following:
Subchapter I- allows for the owner of the trademark to register at the federal level; a trademark MUST meet specific requirements to be registered. A principal person must register the mark, gaining rights to prevent infringement.
Subchapter II - if the mark does not meet the requirements to be registered but still it obviously represents a good or a service in a distinguishable manner, an alternative route is considered and a supplemental registration is allowed.
Subchapter III - establishes what constitutes infringement or dilution of the mark (using it against the rules or copying it and trying to make it look like it is something else).
The requirement is that the trademark falls under one of four categories. It can either be:
- fanciful/arbitrarian- no relation to the product, unique name, such as "Apple"
- suggestive- hints at what the product can do, such as the teeth bleaching products "PearlyWhites"
- descriptive-tells exactly what the place does or is "Pizza Hut", "Kentucky Fried Chicken"
- generic- weak, universal words intended to be trademarked, but with no avail. Ex: "Milk", or "Cheese".
Lanham can only recognize trademarks if they prove to be unique, and if they effectively and uniquely separate the particular brand from all the others. If the name is too generalized, easy to copy and easy to confuse, chances are that you will not get the trademark recognized at the federal level.