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The Lightning Network promises to alleviate Bitcoin's known scalability problems. The operation of such second layer approaches relies on the ability of participants to turn to the blockchain to claim funds at any time, which is assumed to happen rarely. One of the risks that was identified early on is that of a wide systemic attack on the protocol, in which an attacker triggers the closure of many Lightning channels at once. The resulting high volume of transactions in the blockchain will not allow for the proper settlement of all debts, and attackers may get away with stealing some funds. This paper explores the details of such an attack and evaluates its cost and overall impact on Bitcoin and the Lightning Network. Specifically, we show that an attacker is able to simultaneously cause victim nodes to overload the Bitcoin blockchain with requests and to steal funds that were locked in channels. We go on to examine the interaction of Lightning nodes with the fee estimation mechanism and show that the attacker can continuously lower the fee of transactions that will later be used by the victim in its attempts to recover funds - eventually reaching a state in which only low fractions of the block are available for lightning transactions. Our attack is made easier even further as the Lightning protocol allows the attacker to increase the fee offered by his own transactions. We continue to empirically show that the vast majority of nodes agree to channel opening requests from unknown sources and are therefore susceptible to this attack. We highlight differences between various implementations of the Lightning Network protocol and review the susceptibility of each one to the attack. Finally, we propose mitigation strategies to lower the systemic attack risk of the network.