I have a Meyers lemon tree too. I ordered it from Louisiana last year. Good company. It arrived great.
I used to live in Florida for many years. I had a Ponderosa lemon. Huge as a grapefruit! But I couldn't find one for sale so I got the meyers.
As one person said, do not let any branches start below the graft ( its the place down at the bottom that looks a little crooked. Because if you let a branch grow below, it will mess your tree up.
To prune, prune some branches..just a few. And not a hard prune or it will not flower and produce fruit the next year. I learned that the hard way on my grapefruit tree.
So, just prune the leggy long ones. Preferably after the fruit is done growing. You don't need to shock it right now. Do it in steps. Next time, a few other branches until you get the shape you want.
Yes, you will need more light. I am in Arkansas now and have it sitting on my front porch. It gets about 6 hours at least, but don't let this heat get to your plant. It will stress it.
Fertilizer should be 2-2-2. Thats what the company said. And Jobes carries some of those. I prefer vigero myself. I used it in Florida.
Look
online to see if you can order some.
Fertilize 3 times a year.
Your lemons are bigger than mine right now.
I had a huge amount of blooms and a lot were on the same branches. Some will have to come off since it is a little tree. Yours looks ok for now.
And yes that one picture is a new branch. If you want it growing in a good shape, make sure lower branches are pruned.
Make sure it has good drainage.
In florida it rained most every day. But in Kansas, it may be different.
Try to simulate the growing conditions in Florida.
When temperatures get down to the mid 50's, I bring mine in for the winter. You can put a grow light above it. Or a sunny window.
I also have a 12 year old neem tree I bought when it was about 8 inches tall. It is now over 5 foot. I trim it too.
Just make sure it has good sunlight and not bone dry nor too wet.
There are gardens in Italy that have been growing oranges for hundreds of years in pots. Theirs were terra cotta pots (huge too ). They laid theirs down and covered them. ( you probably wouldn't get away with that. Considering how cold and all the snow you get up there. I would bring it in.
When I pollinate, I do it with a sable painbrush, small. And gently dab them in the centers.
Some people use Qtips. I don't because they are too big and it will knock off flowers...
You can buy some of the insulation boards that have the shiny foil color to reflect the light. Or, you can also use foil. To me the boards are easier.
Tying up your tree for now will help with the weight. I use pantyhose (knee highs if you can get away with it. Or I use twine and cushion it for the winds so it doesn't cut into the branches.
Need any more information, message me.
Don't the flowers smell so good? I love mine!
If I can get some pictures to load here I will show you the blossoms. And that was on every branch! But some had to go because of the weight.
I would cut the two lower ones now. And at least the two longer ones after the lemons are done. Each branch pruned will put out two or three.
And watch out for the bugs! I caught one having a feast on mine. So I am going to screen it in I think.