Yes! In the cultivation of lab diamonds, natural conditions are imitated.
HPHT = ✓ conditions analogous to those in the Earth's deep interior
CVD = ✓ conditions analogous to interstellar gas clouds.
During this "growing process" the exact same inclusions can occur as with mine diamonds.
The inclusion types of lab diamonds are also found in mine diamonds. So they are not different/different types of inclusions. Only: a few mine diamonds have so-called "natural inclusions". Analogous to a mosquito in an amber. Such inclusions do not occur in lab diamonds in the "clean" lab environment.
Still, Lab diamonds often even a better color and purity (= quality). Partly Lab diamonds are even harder than mine diamonds because of a better "compression". Nevertheless, inclusions also occur in rennet diamonds.
We also have the impression that with lab diamonds from the best laboratories with excellent quality, the inclusions are often very local and the "rest" of the diamond is "crystal clear", whereas with mine diamonds, small inclusions can often be observed throughout.