Today, it emerged that the upcoming public sector cuts could result in the BBC's World Service broadcasts in Burma and several other countries being scrapped.
Speaking to MPs on the culture, media and sport committee, Lyons said that the corporation is engaged in "robust" talks with the Foreign Office over plans for a reduction in the service's £272 million annual grant.
Lyons also stressed that World Service is "amongst the most valued parts of the BBC's output both in terms of its standing in this country but certainly across the world".
"We're talking about an audience of 180 million in the last year so a very modest expenditure for the BBC and Britain to have its voice heard by that larger audience," he said.
"The BBC is inhibited from using licence fee payers' money for the World Service so any cut that is imposed here actually will be a cut in service - there is no way to avoid that."
At the same meeting, BBC director general Mark Thompson told MPs that the World Service grant-in-aid was "absolutely in scope for the comprehensive spending review".
However, he added: "Manifestly, these are some of the most cost-effective and leanly-run parts of the BBC and significant cuts in grant-in-aid would have a very significant and deep effect on services."
Earlier in the day, culture secretary Jeremy Hunt said the coalition government was "absolutely committed to the global reach of the World Service and the very important job it does as a beacon for democracy around the globe".
He also stressed, however, the importance of reviewing public sector budgets to see if better value could be achieved for taxpayers.