I have a Lennox Pulse 21 model G21Q4/5-100-3. The blower motor will not turn off even if the thermostat is in the off position. I suspect a stuck relay or control. Any advice?

See if you blower speed is set to low speed in the heat mode.
I think what might be happening is the blower is set to low speed in heat and when you switch to automatic, the blower is switched to high speed. You may have to change the blower speed to high in the heat mode. If not you may have an airflow problem such as a Dirty filter, ducts not sized right, dampers on the room outlets closed.

high limit switch, no proof of flame.

Try the fan in the ON position on the thermostat, do you mean the fire shuts off or the blower?

Sounds like the blower motor is getting hot and cycling on internal motor overload. Probably airflow or the blower bearing or capacitor. Turn off all power to the unit then you need to check the filter, Evaporator coil to see if air is getting through it. When checking the coil for a blockage you need to remove a side plate, it's triangular and check the entering air side of the coil to see if its blocked. You need a volt ohm meter with a micro-farad scale to check the blower capacitor and motor amps. You could have a bad motor bearing.

you will need to verify voltage from the board to the inducer. If you have the installtion manual there is a flow chart for the sequence of operation of the furnace.
The basic sequence is:
1. thermostat calls for heat
2. inducer motor starts and runs for a pre-set amount of time
3. the pressure switch closes and allows for ignition trial
4. ignition is proved back to the board allowing the system to operate.

Verify 120VAC to the inducer motor upon call for heat from stat, if you have 120 at the leads that connect to the inducer and it does not start , the motor is faulty. If the inducer starts use a voltmeter across the pressure switch terminals, a voltage reading of 0 VAC will verify contact closure and ignition should occur.

The pulse furnace was under a factory recall due to breaches in the heat exchanger, unfortunately for you, the Lennox Corp. has ended the program that allowed for an allowance / furnace for replacement. To test the heat exchanger a special kit is required from lennox that will verify integrity of the heat exchanger. (If the heat exchanger seal has been comrimised the pressure switch will not prove and the igniton sequence will be interupted and cause the system to go into "lock-out" mode).I know this is probably not what you wanted to hear. Hope this helps, please list as "very helpful" if it did

the next thing you should do is take the green wire off of the t stat that will rule out the t stat then next you should check the fan relay thes units have a fan relay and do go bad

If this is a high eff model, check to make sure the intake vent is not plugged.

Expensive is relative, service calls are never free. But if you have an idea what the problem is, you are armed against an unethical service company. Now to what you describe, could be a couple things, first let me explain the difference in fan speeds. Furnaces that both heat and cool have multi-speed blower motors. High speed is for cooling and lower speeds are for heating. The fan switch at the T-Stat turns on the high speed fan relay. The lower speed fan is turned on by either a temperature activated switch (silver box mounted on front on furnace above burners) or a time delay relay which is solid state. That being said, your problem could be a defective fan switch or one of your blower motor windings has gone bad. Most motors have 3 or 4 speeds and a technician could just change speeds and all would be good. A fan/limit switch is not so expensive that you would replace the unit. Bottom line, unless your really handy, a heating company is in your future. Good luck and please rate my answer if it was helpful to you.  

The bearings are bad. You need to replace the motor. Motor cost $75 to $125. Labor is on avg. $150 to $400 with an decent A/C Company . You can try to oil it but its not recommend by Lennox. That furnace at the time they build it was top of the line. Good Luck.