The establishment of a local lunar time standard or a shared and openly accessible reference timing signal can greatly enhance the positioning, navigation, and timing (PNT) capabilities of lunar missions without the need for direct links to Earth or precision instruments to be a requirement for every mission to the Moon. This paper proposes the concept of a local lunar time standard that can be accessed using technology that is likely to be included in most lunar missions for nominal activities. Even if the local lunar time standard exhibits drift or variations from terrestrial time, its existence would be a significant step towards lunar coordination. Unlike terrestrial synchronized time, a fully usable lunar reference time can be implemented proactively before the activity that necessitates it occurs. This paper discusses the potential benefits and challenges of establishing a local lunar time standard and its implications for lunar missions, including its compatibility with existing lunar initiatives such as LunaNet, Moonlight, and upcoming lunar missions. The proposal highlights the opportunities and considerations for stakeholders in the cislunar ecosystem, including options for missions to ignore, participate in seeding, or consume the proposed timekeeping protocol. The proposal is expected to contribute to the evolving landscape of timekeeping technologies and methods in cislunar space, and stimulate further research and discussion on this topic.