I don't know if this helps but you can put $D=24$ in (13) (14) of my paper to get an explicit formula for $\tau(n)$.

MR2218820 (2007c:17009)  Westbury, Bruce W.  Universal characters from the Macdonald identities.
 Adv. Math.  202  (2006),  no. 1, 50--63.

doi:10.1016/j.aim.2005.03.013 

Since $SL(5)$ is a simple Lie algebra of dimension 24 this also relates $\tau(n)$ to the affine root system of type $A_4$.

I doubt Lehmer would have had this in mind.