LEGO people don't reproduce.
There's a finite number of lego people and parts and all new LEGO people are simply made at a LEGO people assembling building from the disassembled parts of former LEGO people. These parts are usually kept in a giant yellow container curiously called "minifig bucket."
All LEGO people require a triune of parts to be considered alive. The Trunk, the Torso, and the Pineapple ( also known as the yellow head cylinder ). It is only when these three parts are connected that you get a sentient LEGO person.
LEGO people also do not die.
Their pieces do age, their colors do fade... but they don't actually DIE in our sense of the word.
You could compare LEGO to a three-celled organism that only have higher-level functions when all three cells are connected to one another.
Occasionally an accident will happen like a LEGO person hanging onto a helicopter while their torso is clicked into a particularly stubborn pip. When their body is separated, they immediately lose all sentience. While it is possible to put the pieces back together again, once disconnected, the exposure of the innards of the LEGO minifig parts erases all memories and therefore what you could call consciousness so there's really no point.
Effectively they're dead... despite their really being no degradation of the pieces... so their pieces are simply collected and sent to the big minifig bucket in the SKY ( Special Kollection Yard )
When pieces are randomly matched ( or LEGO people are birthed ) all variables are randomized and they gain a completely random personality.
Finite number of LEGO people and the grand purpose
There is a finite number of LEGO people. It will never go higher. It will only gradually get lower over many millions of years as parts wear out and pieces no longer stay together. However, there's a MASSIVE glut of extra parts that have never been used, so that isn't a problem.
There have been some LEGO people who adhere to the teaching of scientism that have proposed bonding pieces together as a means of gaining true immortality, but there is a rather vocal group of religious individuals who feel this is not part of the master builder's plan and that the natural order of disassembly and reassembly is the natural way of things. They fear that permanence is not the LEGO way and goes against their purpose of existence as flexible and modular beings as purposed by the Grand Designer.
They feel that followers of scientism are trying to become The Builder themselves. Many of these scientists don't believe in The Builder and want to believe that LEGO parts came from millions of years of iteration. They refused to believe that their world or their pieces were the product of a designer and feel that their world was not designed, but came about by random accidents in what they call the Big Billund Theory. Although most LEGO people accept most of facts of "Big Billund Factory" the followers of Scientism believe that no being conceived or initiated the "Big Billund Factory" but rather that it came about by accident.
Most LEGO people, OTOH, believe that there was a "First Cause" and attribute it to the "Grand Designer". To many LEGO people, they give this "First Cause" a name. They believe they this Designer is not made of the same materials as them... and use the "Holy Manual" as proof of the Designer's existence. A few call themselves followers of Ole Kirk Christiansen... who occasionally intervenes from a spiritual place called "Denmark". Followers of Scientism say this place doesn't exist and since they can't see Ole Kirk he doesn't exist. As you imagine, it's quite the problem and has caused wars.
Many LEGO people point to the intricate designs as impossible to have come about by mere chance and think the LEGO followers of scientism are somewhat of a cult and as such dismiss them as crackpots. As you can imagine, most LEGO people believe in a Great Designer, though some believe in a pantheon of Great Builders as opposed to one Original Designer.
Note that long ago, LEGO society didn't really exist as minifigs regularly removed the heads and torsos of others randomly, while sleeping... or just out of curiosity. In addition, they sometimes did it to themselves. They could not build a society in those days, and as such were more akin to minifigs wandering in a wilderness of spare pieces.
In the end, LEGO don't reproduce. They simply replace and reuse.