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The meeting aims at bringing observers and theoreticians together towards a joint exploration of the Odyssey that Lyman radiation undergoes as it attempts to escape the galaxy labyrinth. This meeting is motivated by astrophysically important questions, such as: - how is the assembly history of galaxies and evolving physical properties of their multi-phase ISM related to the escape fraction of Lyman photons? - how does the escape of Lyman radiation evolve with the rise and fall of star-forming and accretion-powered nuclear activity in galaxies, and what imprints does Lyman photon escape from galaxies leave on the intergalactic medium and the cosmic web? - what modeling concepts and observational constraints are most needed for achieving a breakthrough in our understanding of Lyman photon escape both at sub-galactic and galactic scales? Thematic units: - Production and transport of Lyman radiation - Reprocessing and escape of Lyman radiation on sub-galactic scales - Lyman photon escape in star-forming galaxies - Lyman photon escape in the presence of accretion-powered nuclear activity in galaxies - Lyman photons in the cosmic web - Challenges and opportunities: observational and theoretical input towards a better understanding of Lyman photon escape over cosmic time