Lost key?

Yes, you would get a set of keys with a new lock cylinder, however replacing the old lock cylinder requires that you can remove the original one, to do that you without damaging the ignition housing you need a working key to rotate the cylinder so it can be removed. As you don't have that you would need to then move to replacing the complete ignition switch assembly. That means removing the trim around the steering column and then the column itself. Then with the column out you cut the original bolts off to remove the retainer. Then you install the replacement and then reverse the removal process. Now you have a car with new keys, that still requires either the locksmith to come and program them into the system or a trip to the dealer for the same thing. With changing the cylinder you would still need to change out the door locks to be able to use the key. Plus being you have no working key or a working fob, there is no process for you to add a new FOB to the system. Unfortunately the locksmith is likely the best option of the two. However I would have them make 2 new keys and while they program those in you make sure they erase all the old keys for the car. That way none of the original keys can be used on it should the original you had or the others that came with the car be located. This is VERY common with newer vehicles when all the keys are lost as the key isn't just a key any longer, there is a chip in them that deals with the security system and can also be used along with that for other functions. Same thing with the FOB that many cars now use for everything. The one for your car had different options available but the basic one just locks and unlocks the doors. The next one also does remote start but it still requires a working key to keep the engine running and allow the rest of the car to operate, as the remote start only starts the engine. When you get in you put the key in and turn it to run and now you have the ability to put the car in gear and have the instruments and things like the heat and radio will now work. Without the key you would get in, shut the door and if you try to put the car into gear the engine shuts off.
There really is no way around the two options you already know about.

Yeah, the issue is that many people get blindsided when it comes to newer vehicle keys because of the security constraints on them. There have been a lot of systems used and each is a little different, to the point that even locksmiths and dealers have cheat sheets these days so they can keep them apart. As an example, some let you program in keys while using two good keys, then others require a scan tool to add any keys, still others require at least one known key and a scan tool and those are all the same brand of vehicle! It can get frustrating just keeping them all straight. Then you go online and get 5 different answers and decide "Well I'll just do this" and then discover you may have made it even worse.
Normally in a case like this the smith will either call the company, give them the vehicle info and his security ID and they will give them the code used to cut the key. They then cut it and verify that it does rotate the locks, then you program the key in and if it all works, you then cut a second one and then erase all keys and add only the 2 new ones. Or they will use a tool like a Lishi to decode the lock in the vehicle and then cut from that code. I prefer the second option myself because who knows for sure that someone hasn't swapped a cylinder already.