The existence of compact stellar remnants in the mass range 2–5 M ⊙ has long been debated. This so-called lower-mass gap (LMG) was initially suggested by the lack of low-mass X-ray binary observations with accretors about 2–5 M ⊙, but it has recently been called into question following newer observations, including an LMG candidate with a millisecond pulsar (MSP) companion in the dense globular cluster NGC 1851. Here, we model NGC 1851 with a grid of similar dense star clusters utilizing the state-of-the-art Monte Carlo N-body code Cluster Monte Carlo, and we specifically study the formation of LMG black holes (BHs). We demonstrate that both massive star evolution and dynamical interactions can contribute to forming LMG BHs. In general, the collapse of massive remnants formed through mergers of neutron stars (NSs) or massive white dwarfs produces the largest number of LMG BHs among all formation channels. However, in more massive clusters, supernova core collapse can contribute comparable numbers. Our NGC 1851-like models can reproduce MSP—LMG BH binaries similar to the observed system. Additionally, the LMG BHs can also become components of dynamically assembled binaries, and some will be in merging BH–NS systems similar to the recently detected gravitational wave source GW230529. However, the corresponding merger rate is probably ≲1 Gpc−3 yr−1.