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Hi I'm Brian and I'm here to help!
The Lennox CBX air handlers when matched with the Lennox XC14 condensing unit can indeed be used with standard heat/cool thermostats. Whether or not the Honeywell 4000 series you are looking at can be used depends on which model. One of them is for conventional heat/cool units (TH4110D) and the other is for heat pump systems ONLY (TH4210D). You need the TH4110D for your system since it's not a heat pump.
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Further, if you currently have a Lennox Icomfort Touch thermostat, you will need to rewire the low voltage in the air handler and possibly the condenser for standard thermostat usage. You will also need a minimum of four wires between the thermostat and air handler which you should have anyway if the system is using an Icomfort Touch control.