Short answer, it might work. But for how long?
Here is a longer answer.
There is an app for your phone called Ohm's Law, it's free. You need it to answer questions like this about using 120 volt things on twelve volts, like we do in our vans / rv's.
When you have a 120 volt item you want to run on twelve volts, you only have 1/10th the voltage (12 volts) and amperage of what it is designed to run on (120 volts).
In that Ohm's law app, first you enter the voltage, 120 volts.
Second you enter the watts, sometimes referred to as power, 90 watts.
The calculation is made and you see it is using less than 1 amp...750mA.(mA stands for milliamp...1000 milliamps equals 1 amp)
Now you change the number in the voltage to 12 and you see change in the current / amps.
It changes from 750mA to 7.5 A. What the app has done is multiply the amperage by 10 because the voltage entered represents 1/10th that of 120 volts. This is the relationship 12 volts has to 120 volts.
Watts however stays the same.
The 7.5 amp draw is what the little crockpot needs to operate on 12 volts where it only needed 3/4 of an amp (750mA) when plugged into 120 volts. Ten times more of those 12 volt amps than the 120 volt amps.
Think of watts as the "Price". Let's call the price a dollar. With 120 volts, you pay with a dollar bill. With 12 volts, you pay with ten dimes. In either case the price you paid was a dollar. Does that make sense?
If the 150 watt inverter is capable of producing at least this much amperage, then it should be able to run the little crockpot.
For how long?
The little crockpot is using watts over time. So many watts over so much time.
This is expressed in Watt Hours (Wh).
The little crockpot uses 90 watts over one hour of time.
Depending on where the inverter is getting its power the length of time the little crockpot is able to operate will vary.
If you intend to run the little crockpot using the battery power in your van, the question is how much power can your battery provide before being discharged?
Using that Ohm's Law app again, clear the numbers, reset, and enter 12 in the voltage box, enter 100 in the Current or Amps box and the other boxes fill in. The power or Watts box show 1.2kW or 1200 watts.
Of this 1200 watts, with normal lead acid, agm, etc. batteries, only 50% of these watts are actually usable without harming the battery.
Back to the Ohm's law app.
Clear the boxes, reset, and enter 600 in the power or watts window.
enter 12 in the voltage window.
The current or amps window fills with 50.
So fifty amps is what you can safely draw from the battery.
Now open your calculator app.
Enter 50 and divide it by 7.5, the number of amps the little crock pot uses per hour.
The result is 6 and two thirds.
So in a perfect world, you could run the little crockpot for 6 hours and forty minutes.
But the world isn't perfect. All kinds of losses exist that will take this "run time" down significantly.
If your use case includes solar panels and you use the little crockpot during the day when the power generated by the solar panels is enough to keep up with charging the battery(s), while using the little crockpot, in other words, more than 7.5 amps, then essentially you could run the little crockpot using the energy of the sun and the battery(s) would be at capacity until the sun no longer provides the power.
Bear in mind, a 100 watt solar panel might at best produce 5 to 7 amps so you would likely need more than this to run the little crockpot AND keep your battery(s) charged up.
I hope this helps you in the future to answer this sort of question we have when trying to power different items we want to use in our vans / rv's