Triple-negative (ER^-PR^-HER2^-) breast cancers (TNBC) are highly aggressive and difficult to treat. TNBC exhibit high genomic instability, which enables them to adapt and become resistant to chemo/radiation therapy, leading to rapid disease relapse and mortality. The pro-survival factors that safeguard genome integrity in TNBC cells are poorly understood. LBH is an essential mammary stem cell-specific transcription regulator in the WNT pathway that is aberrantly overexpressed in TNBC, correlating with poor prognosis. Herein, we demonstrate a novel role for LBH in promoting TNBC cell survival. Depletion of LBH in multiple TNBC cell models triggered apoptotic cell death both in vitro and in vivo and led to S-G2M cell cycle delays. Mechanistically, LBH loss causes replication stress due to DNA replication fork stalling, leading to ssDNA breaks, ɣH2AX and 53BP1 nuclear foci formation, and activation of the ATR/CHK1 DNA damage response. Notably, ATR inhibition in combination with LBH downmodulation had a synergistic effect, boosting TNBC cell killing and blocking in vivo tumor growth. Our findings demonstrate, for the first time, that LBH protects the genome integrity of cancer cells by preventing replicative stress. Importantly, they uncover new synthetic lethal vulnerabilities in TNBC that could be exploited for future multi-modal precision medicine.