Lemon Tree

1-Yes, a lemon tree can thrive in a pot and even produce some nice fruit.

2- Sort of. The problem with growing fruit from seed is that they do not come "true". That means the fruit of the new tree will probably not taste like the fruit from which it came. Sometimes you get very, very lucky and it tastes better. When that happens, growers graft it to make more of that same tasting fruit.

You are best off buying a small tree. Meyer lemon is reliable and you can usually find them for less than $20. Big box stores like Lowes or Home Depot often have them this time of year

How big of a pot would I need?

I have no clue how large a lemon tree would grow..
Is there some sort of magical ratio to use?

Like.. 1 foot of tree to 3 cubic feet of soil.. or something like that..?

I kept a meyer lemon tree for years in a half barrel....

You have to "bonsai" them. You can probably start with a one-two gallon sized pot. As the plant grows you can go up a pot size or two, but each time you bump it up you will trim the roots and put in new soil. You also have to fertilize on a regular basis. An indoor tree can be pruned to keep the size reasonable. I have a 8 year old key lime that is only about 4 feet tall and about 2 feet wide, if I planted it in a Florida garden it would probably get to be about 10 feet high (or more) and 8 feet wide. It happily lives on my patio in the summer and in my sunroom in the winter.

I've had very good success with the plants from this mail order nursery and their growing instructions:

Raintree Nursery - citrus trees