\version "2.19.44"
\header { tagline = ##f }

\relative {
  \time 8/8
  a'4 ^\markup { LP’s default for 8/8 } a a a a8 a a a a a a a a1
}

\relative {
  \time 4/4
  a'4 ^\markup { LP’s default for 4/4 } a a a a8 a a a a a a a a1
}

\relative {
  \time 2,2,4 8/8
  a'4 ^\markup { I can make it do this (as wanted) easily } a a a a8 a a a a a a a a1
}

\relative {
  \time 2,2,4 4/4
  a'4 ^\markup { Can I replace “2,2,4” with something else? } a a a a8 a a a a a a a a1
}

\relative {
  \set Staff.timeSignatureFraction = 4/4
  \time 2,2,4 8/8
  a'4 ^\markup { or must I hack it like this? } a a a a8 a a a a a a a a1
}

\relative {
  \overrideTimeSignatureSettings
  4/4        % timeSignatureFraction
  1/4        % baseMomentFraction
  1,1,2      % beatStructure
  #'()       % beamExceptions
  \time 4/4
  a'4 ^\markup { or write it verbosely like this? } a a a a8 a a a a a a a a1
}