Recently, a new coronavirus disease COVID-19 has emerged as a respiratory infection with significant concern for global public health hazards. WHO was alarmed with the growing curve of confirmed cases and death tolls that have been globally reported. During this pandemic, ‘social distancing' and lockdown were encouraged to flatten the curve which has had major social, political, and economic consequences. Drawing on data from PM Boris Johnson's and President Donald Trump's public speeches after WHO's declaration of the pandemic state, the current study aimed to explore the conceptual and spatial representation of lockdown during the outbreak of COVID-19 in the UK and U.S. from a cognitive perspective. Based on a spatial-temporal and axiological model, this study examined the discursive strategies used by the UK and U.S. governments to legitimize the countries' full or partial lockdown. Applying Cap's Proximization Theory, a cognitive-pragmatic model of threat construction, this study investigated how these administrations constructed threat by deploying construal of relations between entities within the Discourse Space. The findings revealed how DS between the conceptualizers' deictic centre and the threat was curtailed or broadened using conceptual, lexico-grammatical, and coercive strategies. The results showed that PM Johnson relied heavily on a dynamic discursive representation of threat; whereas, President Trump represented the Chinese threat statically. The former appealed to conceptualizers' fear by broadening the distance between the threat and conceptualizers using promising proximization; whereas, the latter downplayed the virus' risk blaming it on others, positioning adversary state(s) as source of threat in mental space.