This seems to be a poster from the British Empire asking for support from the "young lions," which would be Australia, Canada, India, and New Zealand, to support the "old lion," which would be Great Britain. In this case, the support would most likely be to either defend the British Empire or to expand it, in any capacity, it means supporting the Empire.
There were several events that led up to the creation of NASA, but the biggest was the space race with Russia, which was especially heightened after Sputnik.
