Here's some solution, but less than ideal. I'd prefer to use unicode for the 1/2 symbol, but the time signature font didn't seem to support it. I think you want some basic time signature as I've put (5/8) and then change the text of that, positioning the 1 and 2 in the 1/2 and drawing the line inbetween.
myTwoAndHalfTimeSig = {
\once \override Staff.TimeSignature.stencil = #ly:text-interface::print
\once \override Staff.TimeSignature.text =
\markup \override #'(baseline-skip . 0) \center-column \number {
\concat {"2" \magnify #0.5 \pad-x #-.2 {
\translate #'(0 . 1) "1"
\translate #'(-1 . 0) \override #'(thickness . 2) \draw-line #'(1 . 2)
\translate #'(0 . 0) "2" }} "4" }
\time 5/8}
right = \relative c' {
\myTwoAndHalfTimeSig
c8 c c c c
}
left = \relative c {
\myTwoAndHalfTimeSig
c8 c c c c
}
