Depends on what you are willing to compromise on, and how much you want to spend.
Decreasing the amount of ambient light by half is a lot cheaper than buying a projector that is twice as bright. Brightness, contrast, price, pick 2. A 150" screen is quite large. Most projectors cannot project a useful image of that size with that much ambient light. Regardless of the projector you choose, if you project a smaller image during the day, it will be a lot brighter and a lot less washed out. Then you don't need so many lumens, and you can still project a 150" image when it is dark.
If daylight viewing is important to you, Epson LS100 might be worth considering. It has a lot of lumens for a projector under $3000, and it uses laser. With laser, you do not need to spend money on replacement lamps, and you won't have to deal with lamps dimming towards end of their life. Most other projectors use lamps, with expected life between 3000-5000 hours. This life is based on how long it usually takes for a lamp to become half as bright. If you need as many lumens as possible, you might need to change lamps even sooner.
* 4850 lumens in Dynamic Mode
* laser light engine lasts 20,000+ hours
* UST (ultra short throw)
* fan noise is a non-issue, because projector is placed close to the screen, and far from viewers
* you can pair it with an UST ALR screen, which is expensive but makes a big difference with ambient light
* projected image can be no larger than 135" 16:10 (130" 16:9)
* 1,030:1 on-off contrast is less than other popular HT projectors like Epson 5040UB
* not 4K