The lionfish invasion in the Atlantic and Caribbean has proceeded with vigor since their introduction in the 1980s or early 1990s. Lionfish affect recruitment of juvenile fish to reefs due to predation and are found in densities far surpassing that of their native Indo-Pacific. There is concern that the lionfish may become introduced and proliferate (through aquarium releases, transport on floating debris, or passage through the Panama Canal in ship ballast water) in the eastern tropical and north Pacific. This study presents the first known prediction of the potential for establishment of lionfish in the eastern Pacific Ocean. Through computational modeling, we compare and contrast the dynamics of random hypothetical introductions of lionfish into the eastern Pacific and Atlantic Oceans in order to highlight the different potentials for invasion in both basins. Connectivity between discrete regions (precincts) in both the Atlantic and eastern Pacific are examined and settlement densities are calculated to indicate possible locations of establishment of breeding lionfish populations. Our results suggest that lionfish, which are successful invaders in the Atlantic, may not be as successful in the eastern Pacific due to weak mesoscale connectivity which reduces the rapid spread of lionfish larvae.