Can you take a look in the furnace and verify that all the wires are to the correct terminals?
red should be on RH, green should be on G, yellow should be on Y, white should be on W. The blue or the black may be the common, should be checked to make sure as it isn't the normal color for that.
Anyway, assuming all the wires I mentioned are on the correct terminals, on the Lux thermostat, connect the red to RH, the green to W, yellow to Y. Then run a jumper wire from the RH in the Lux to the RH in the round honeywell. Also connect the white wire to the W in the round thermostat.
After checking in the furnace if there is a wire on the C terminal, connect that to the C in the new thermostat also. If nothing is on it and those two wires aren't used, you could connect one of them at both ends. Otherwise you will need batteries to power the thermostat. If it doesn't have that option then it just won't work.