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Trees often lose leaves and/or turn brown when they're indoors for the winter, because it's difficult to give outdoor plants enough light indoors, and the humidity level can also be a problem. However, most of these plants will come back in the spring. Try moving your plant outside gradually so it has time to adjust, as explained in this article:

https://www.gardeningknowhow.com/houseplants/hpgen/move-houseplant-outside.htm

Also, be sure not to overwater the plant until it starts growing again. Check the soil each time and water when the soil is dry, but don't let the soil stay soggy.

Lemon Cypress trees do need quite a lot of water, especially in pots. Make sure to water this new one whenever the soil starts to dry out. Do let it dry out, though - it's easy to overcompensate and accidentally drown a potted plant.

Maybe even more important that water is light. Lemon Cypress trees need lots of sun and really don't do well in the shade. Make sure it's in a place that gets full sun.

This article should help you more with the ins and outs of Lemon Cypress care: https://www.gardeningknowhow.com/ornamental/trees/cypress/lemon-cypress-care.htm

We do not sell plants on this site, we provide garden information.

Check with your local garden centers and greenhouses.
Do a Google search for sellers; as they may ship directly to you.

https://www.gardeningknowhow.com/ornamental/trees/cypress/lemon-cypress-care.htm

Give them as much light as possible, and they may come back. This plant typically needs a lot of water, but in their weakened state they won't be using much, so make sure the soil doesn't stay too wet (but doesn't get bone dry either). Here are more tips for caring for lemon cypress:
https://www.gardeningknowhow.com/ornamental/trees/cypress/lemon-cypress-care.htm

And here's how to tell if a plant is dead:
https://www.gardeningknowhow.com/ornamental/trees/tgen/tree-scratch-test.htm

Grump tree is often lemon cypress. If it is in the container from Trader Joe's, repot to a larger pot using a quality potting soil mix. Soak the plant weekly and water in-between soaks if the indoor air is drying it out quickly. It must have bright sunlight; turn the plant frequently so a different side gets sun. If your area doesn't receive bright sunlight, use supplemental lighting.
https://www.gardeningknowhow.com/ornamental/trees/cypress/lemon-cypress-care.htm

You can use all purpose potting soil. That will be just fine. I cannot find any literature on it being poisonous to pets... But it may cause skin irritation at most. I don't see it being a problem. Here is an article that will give you more information: https://www.gardeningknowhow.com/ornamental/trees/cypress/lemon-cypress-care.htm