Caves were used to store the beer for months on end at pretty low temperatures.
To produce a true Lager you need to replicate that process but with modern methods.
We have fridges etc to achieve this.
Basically there are two types of yeast:
a) Ale yeast as used by british brewers
b) Lager yeast as used by continental brewers
Ale yeast ferments on top of the beer and once finished fermenting floats to the bottom of the fermenter.
A true lager yeast ferments at the bottom and stays there throughout the fermentation process.
Ale yeasts are typically fermented at between 18-20c. Any higher and you start to get funky/fruity flavours which sometimes are benificial but only if that is the kind of taste You are looking for. Higher temps also produce the hangover forms of alcohol which We really want to avoid.
Lager yeast will typically be fermented between 12-18c. Once the main fermentation process has completed after around 4 days or so the wort is cooled to around 4c and Lagered for weeks and months depending on how much patience You have.