Building the environment is not so difficult, just a boiler, a water pump and some mud. The production of the acid-basic gradient is more difficult. You need some chemical compounds, they are neither rare nor expensive, but you will probably need a lot of them to run a long time experiment. (Perhaps it's easier than what I'm imagining now.)

It's very difficult to build a LUCA, in particular no one knows exactly how it looked, no one knows the DNA, no one ... There are examples of genetically modified bacteria, but they have only small changes, this is more difficult. You must cut all that looks modern and hope that the remaining cell is capable of surviving. Maybe add some other genes that look useful. I think that this is almost impossible with the current technology and knowledge.

Another possibility is to just build the environment and throw some mud and hope that something survives (perhaps it'd be easier with mud from a similar natural place). The problem is that probably modern bacteria or modern archea have evolved to live there and have eradicated the first LUCA versions completely. So it's difficult to find the original living thing, but perhaps the modern replacements can give some insight about the old thing.