There has been limited review of the reported deployment of infusion pumps in low- and lower-middle-income countries. This paper aims to identify the current distribution of infusion pumps in low- and lower-middle-income countries (LLMICs) used to treat neonates. A rapid review was conducted using material sourced from ProQuest, Pubmed, Web of Science, and IEEE Xplore. Twenty-six search results met the inclusion criteria. Within these, 41 neonatal healthcare facilities were discussed with 17 of the facilities having infusion pumps available, 13 limited access, and 11 none. Infusion pump use remains limited in Sub-Saharan Africa so efforts should be made to deploy specialist neonatal care improvement packages, potentially including infusion pumps designed for LLMICs. The effects of COVID-19, to neonatal care LLMICs, should be accessed to ensure progress has not regressed. These proposals aim to aid in the continued improvement of neonatal care globally and reduce newborn mortalities.