One can build cues with their Boy Scout pocket knife and a hunk of wood to get started if that's where you want to begin.
The question is...where do you want to end up? Do you want to just build 300$ cues to sell to your friends and family that you have 295$ invested in time and materials? Or would you actually like to pay some bills and replace and restock inventory without having to go into your startup pocket again?
Oh yea....you can buy a lathe to "get started" but the rabbit hole is a very deep one.
Tooling...... Just using my shop as an example, roughly 30K in machines ( mostly purchased in the used market) ....probably have close to that in tooling alone. Some are one time buys, some need to be replaced as they get used up.
All of this started over 25 years ago with the purchase of a 100$ metal lathe that was found stuck in the corner at a local machine shop.
The more quality you desire in your end product the higher your quality of machine/tooling costs will climb as will the desire for more space in your shop.
Buying just "1" lathe and setting it up for all of the different operations needed to complete a cue you will soon find out is a major pain in the ass.
This is just the beginning.
Wood....go buy enough wood to build a cue. Better make that enough wood to build 2 or 3 because chances are your first 1 or 2 are going to be mistakes that you end up giving away or using for something entirely different than playing pool with because they wouldn't stay straight.
The learning curve.... even if you start with basic machining skills you will make up words that no young child should ever hear come from your mouth when you turn your beautiful master piece into a wasted piece of shit because you weren't paying attention and forgot to set something correctly or turn a dial the right way because you were distracted by something or someone.
The amount of wood you will need never ends. Just matching 2 shafts alone you may need 25 to find 2 that weigh the same, have the same flex response and are close in tone quality. Learning how to keep a one inch dowel that you are going to turn down to roughly a half inch in diameter straight and being able cut it without having to sand the crap out of it to get the tooling marks out is always a challenge in itself.
Joint pins, glue, leather wraps, linen wraps, phenolics, more tooling because you don't already have enough.
Finishing material...how are going to finish your cues? Do you want the finish to last for years or just a few months? Do you just want a coating that is shiny but still full of polished scratch marks or a coating that looks like a piece of polished glass?
Learning these things and perfecting these things are two different animals. It takes time, it takes a willingness to achieve, it takes a desire to build every cue that you have finished to be better than the last one you completed.
The whole process will either become an addiction or a pain in the ass that you wish you would have never gotten into!
Which ever direction it takes you in, good luck.