Using lc instead of lt in the code you posted works fine with version 4.6.5:
reset set style rect back fs empty border lc rgb '#008800' set object 1 rect from 1,1 to 2,2 lw 5 set object 2 rect from 1,3 to 2,4 lw 5 fs empty border lc rgb '#880088' plot x

In any case (both with lt 3 and lc ... ) the borders of the rectangle are solid. I tried the terminals wxt , pngcairo , pdfcairo and postscript and set the dashed parameter each time.
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