BBC3 and BBC4 are thought to be under threat as the Beeb attempts to make savings of £300m.
Lyons says efficiency savings alone will not be sufficient to meet the funding gap and that "hard choices about content and services" will be required in the wake of last year's licence fee settlement with the Government.
He says the Corporation should concentrate on "doing fewer things better" – prioritising BBC1, BBC2, Radio 1 and Radio 2 – but made no mention of any of the BBC's digital TV or radio services.
Sir Michael's comments were published today in an open letter to BBC director general Mark Thompson, who will tomorrow address BBC staff on the implications of the cuts.
The BBC's income will be at least 16% lower in 2016 than it will be in 2011 as a result of the funding settlement in October, which saw the licence fee frozen at its current level of £145.50 per year.
Last year BBC 6 Music won a reprieve after a public campaign to save it.