Lemon tree is succeeding

My brother, who was blessed with lemon trees on his property as he bought it. He gave me a a sack full of lemons last year. I tried 6 seeds. 5 have failed at one point or another in same planter. Transplanted remaining 1 in a larger container. Its taken off finally. About a foot tall with leaves abound. Its in a typical planter pot about a foot tall pot. Have another planter pot twice the height and width.
My intentions are get it to grow until its around 4 foot before transplanting to the front yard. Read someplace last year, lemon trees are good for 2 transplants. I want more height so dogs don't bother it. Should I transplant ot the next larger planter pot, OR, transplant to where I want it to be in the yard next time? Dave

Dave
I do not have the answer to your question but this information also pertains to citrus trees.

Appreciate your help. Need a more specific answer regarding the specific information I provided. Dave
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Generally, a single transplant is best, less root disturbance. I would suggest that on a question like this, a general location would help, you could run into some site problems if too far off the better climate range for lemon. At the size you are representing, planting out now should not hurt, but again, like real estate, location, location, location.
Beware so called "tree biologist" that have never studied biology.

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The final location's native soil will make or break the tree. Central TX, fractured limestone/caliche/minor clay topsoil depth minimum. 20 degree incline, front yard. 8" of topsoil consisting of sandy loam and some pine bark. The climate is appropriate, however.
Tree started in a large mixed combination of "topsoil", "potting soil", and some minor fertilizer. Switched to current planter. Soil is red clay and sandy loam mix with minor fertilizer added. Thrives in that.
Can't and won't transplant until tree is at least 4' in height. Its intended location is front yard. One of 2 dogs will tear it up if a minor sapling. Fencing is inappropriate, the dog mentioned will tear it down or dig under the fence eventually. 3rd season try for a papershell pecan has taught me all this. The dog stays. Dave

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Central Texas tough on any transplant, good luck.