If you use the following acaddoc.lsp file (acadlt.lsp in LT), the current measurement unit will show up in the cad taskbar.
Download acaddoc.lsp and save it into your support directory (rename it to acadlt.lsp in LT). If the file is already present do not overwrite it, just copy and paste the following code at the end of the original one with any text editor.
command: n/a
(SETVAR "modemacro" "UNITS: $(index,$(getvar,insunits),\"-,in,ft,mi,mm,cm,m,km,µin,mil,yd,A,nm,µm,dm,dam,hm,Gm,au,ly,pc\")")