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It's not a good idea to plant a lemon tree in a lawn area. It's not because of full sun or fertilizer, but the irrigation that a lawn requires is too much for a citrus tree and will cause root and crown rot.

It's best to plant a citrus in a designated planting area where you can create conditions and water management that is appropriate for citrus.

It' not a good idea to plant a lemon tree in a lawn area. It's not because of full sun or fertilizer, but the irrigation that a lawn requires is too much for a citrus tree and will cause root and crown rot.

It's best to plant a citrus in a designated planting area where you can create conditions and water management that is appropriate for citrus. They prefer slightly acidic, well-drained soil. Water deeply about once a week.

Here's more:
https://www.gardeningknowhow.com/edible/fruits/lemons/how-to-grow-a-lemon-tree.htm

Lemon tree suckers are common and should be removed so as not to steal nutrition from the parent tree. If planning to replant a sucker, it most likely won't be the same as the parent if it is a grafted tree.

You can trim the root and it should enourage more roots to grow.

https://www.gardeningknowhow.com/edible/fruits/lemons/suckers-on-lemon-trees.htm

You may have heard of poke weed. Whatever you do, don't eat any part of it. The whole plant is toxic, especially the roots. Here is more information:
https://www.gardeningknowhow.com/edible/vegetables/pokeweed/controlling-pokeberry-plants.htm

If you are feeding it, then check and make sure that it contains enough phosphorus and potassium. Feed with too much nitrogen will half flowering.

If you do not feed it, then it is likely that it doesn't have enough phosphorus and potassium in the soil.

This article will help: https://www.gardeningknowhow.com/edible/fruits/lemons/no-flowers-on-lemon-tree.htm

Alternatively, if it were pruned too heavily when it was young, you could have lost the top graft, leaving you with only the rootstock. Most commonly the rootstock is 'Flying Dragon' which is hardy but will not fruit. On the rare occasion that it does fruit, they are not edible, at all.

Make sure to check and make sure that all growth comes from ABOVE the graft knot close the the base of the tree. If any of these shoots come straight out of the ground, then they are likely the rootstock and not the tree that you purchased.

Probably sooty mold growing on the honeydew excretions from an insect pest, aphids or scale. The sooty mold is not pathogenic/harmful. Control the insect pest and eventually the sooty mold will clear up.

https://www.gardeningknowhow.com/edible/fruits/citrus/sooty-mold-on-citrus-trees.htm

Depending on the type of lemon, and where it was grown, along with which pollinator they used, you may never see a fruit from your lemons, or it may be bred with a wild type leaving you with an inedible fruit. Sometimes they breed true, sometimes they don't.

However, you should still see flowers anywhere from 6 years to 10 years, depending on its lineage. This article will help you to grow lemon trees properly: https://www.gardeningknowhow.com/edible/fruits/lemons/how-to-grow-a-lemon-tree.htm

Papaya is a different story. You have three types- Male, female, and bisexual. The first two types need both in order to pollinate and fruit. The last option (which most are) is self fertile. You should see flowers at about 6 months or so from seed. They flower relatively fast. This article will help you to care for the tree: https://www.gardeningknowhow.com/edible/fruits/papaya/growing-papaya-fruit.htm