Q.Just planted a new lemon tree, and I want to know how to care for it?
It is about 4 ft tall and had numerous lemons on it. The leaves are shriveling up, so I removed the lemons after a few weeks, thinking that the tree needs to get established. I live in northern Calif and there has been no rain for weeks. Watering the tree twice a week. How can I make sure it survives?

Yes water management is a key issue. Getting that right is the most important thing.
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/testing-moisture-in-plants.htm
From the photo, there appears to be some nutrient deficiency, indicated by the yellowing on some of the leaves. A slow release organic fertilizer specific for citrus will help, like this:
https://www.downtoearthfertilizer.com/products/blended_fertilizer/citrus-mix-6-3-3/
In Santa Rosa area you will need to be concerned about frost damage and protecting the tree when a hard freeze is predicted, which is possible December through mid March.
Here is an article with more information:
https://www.gardeningknowhow.com/edible/fruits/lemons/growing-lemon-trees-containers.htm