Reputation systems and distributed networks are increasingly common. Examples are electronic marketplaces, IoT and ad-hoc networks. The propagation of information through such networks may suffer delays due to, e.g., network connectivity, slow reporting and rating-update delays. It is known that these delays enable an attack called the reputation lag attack. There is evidence of impact of reputation lag attacks on existing trust system proposals. There has not been in-depth formal analysis of the reputation lag attack. Here, we present a formal model capturing the core properties of the attack: firstly, the reputation of an actor failing to reflect their behaviour due to lag and, secondly, a malicious actor exploiting this for their personal gain. This model is then used to prove three key properties of the system and the attacker: if there is no decay of reputation, then the worst-case attacker behaviour is to cooperate initially, then wait, then behave badly; increasing communication between users was found to always be of benefit to the users; performing a specified number of negative interactions given any instance of the system is an NP-hard problem.