Background: Sri Lanka diagnosed the first local case of COVID-19 on 11 March 2020. The government acted swiftly to contain transmission, with very stringent measures for social distancing: complete island-wide lockdown, contact tracing and isolation, and quarantine of all inbound passengers were all adopted by 20 March. In the first 30 days, Sri Lanka has had 197 cases with 7 deaths, and is now considering a staged relaxing of the lockdown. This paper proposes a theoretical basis for estimating the limits within which the reproduction number should be constrained, in order to ensure that the COVID-19 case load remains within the capacity of the health system of Sri Lanka, while the infection spreads slowly. Methods: We used publicly available data and adopted a Susceptible, Infected, Recovered (SIR) model to explore the number of new infections and estimate ICU bed requirement at different levels of R0 values after a lockout period. We considered the entire population of the country exposed, with a 14-day period of infection. We assumed 50% of the infected are symptomatic, of which 5% would require critical care, and that the maximum national capacity for treatment of such patients would be 300 beds in Intensive Care Units. Results: The cumulative case load increased exponentially during the first 8 days of the epidemic and started flattening out from day 9 in the country. In a lockout situation, if the number of infected doubles every 20 days (R=1.5), at least 300 ICU beds are likely to be required by the end of 100 days. If the number infected doubles every 14 days (R=1.7), the ICU bed capacity is likely to be exceeded in 70 days. This period is reduced to 50 days if infected cases double every 10 days (R=2.0). Conclusion: Our model suggests that the desired level of control post-lockout to ensure that the case load remains within the assumed capacity of health system lies somewhere between R=1.5 and R=1.7, where the period for doubling of total infections would be 14 - 20 days, and the number of new infections would be between 16 and 24 on Day 7, and between 20 and 34 on Day 14. This model can be refined to suit other low and middle income countries which may contemplate lockout, but have similar health resource constraints.