How do I get 150F water to the dishwasher?
You don't. Let the dishwasher do it for you.

I have read in a maintenance manual that the ideal temperature for incoming water to a dishwasher is 150F.

Was it a maintenance manual for your actual dishwasher? If not, I would ignore random advice (no better than advice from some stranger on the internet...).
Most dishwashers now automatically heat water as needed to the necessary temperature for optimum performance. This avoids exactly the problem you mentioned - water hot enough to clean effectively and to sanitize dishes is also hot enough to quickly burn people. Some dishwashers (I think typically European models) are even designed to run with cold water - heating water from cold to very hot as needed, not just hot to very hot. That being said, I would recommend connecting your dishwasher to the hot water line rather than the cold water line, unless your manufacturer specifically recommends otherwise, because:

Electric heat is generally more expensive than natural gas or other forms of heating. If your main water heater is electric then any heating by the dishwasher will cost the same as your main water heater, and if your main water heater is something else then any heating by the dishwasher will cost more. I can't see any normal scenario where using your dishwasher to heat from cold to hot will actually save any money.
If your dishwasher runs some cycles without heating the water to very hot (e.g., perhaps a regular rinse cycle as opposed the main wash cycle or a final sanitary rinse cycle) then using hot water instead of cold water will be much more effective.