Do I need a regulator to connect a tankless water heater to a 20 lb. propane tank?
@Pigrew is right in the comments.  My previous answer was wrong and dangerous. Do not supply 30 psi of propane to a tankless water heater. 



New Answer:

According to Rheem (a manufacturer of tankless gas water heaters) and The West Virginia Propane Gas Association, modern homes have a 2 psi supply line from the meter with regulators on each piece of equipment to lower the pressure more.  Older homes could have a much lower pressure from the meter negating the need for regulators on each piece of equipment.

Pressure in a propane tank, large or small, can range between 100 and 200 psi.

An example tankless water heater specs list a maximum gas pressure of .5 psi. 

Once we get into pressures this low, people start using the unit inches of WC (Water Column) instead of psi.  The standard pressure that household appliances typically need is 11" WC.

You will need two regulators.

You will need one regulator to take the tank pressure (up to 200 psi) to down to a household line pressure (2psi).  You will also need a regulator to take the household pressure down to the 11" WC needed by your hot water heater.  The reason you need two is because that is a large pressure difference and there are limits to the abilities of regulators. 

There is a bit of fudge factor though.  You could get a regulator that outputs 10 psi fir the first one if you can get a regulator with an inlet pressure over 10 psi (and outlet pressure of 11" WC) for the second one.

There is another factor to consider when choosing a regulator: flow rate.

All of this adds up to the suggestion that you call a professional because explosive compressed gas in your home where your family sleeps isn't the best thing to be playing around with.