Final answer:
A lack of extracellular Ca²⁺ would not cause increased release of neurotransmitters but would impede the process and result in decreased neurotransmitter release, making the statement false.
Step-by-step explanation:
The statement that a lack of extracellular Ca²⁺ would cause increased release of neurotransmitters is false. Calcium ions (Ca²⁺) play a crucial role in the process of neurotransmitter release at the synapse. When an action potential reaches the axon terminals, voltage-gated calcium channels open and allow Ca²⁺ to enter the cell. This influx of calcium ions causes synaptic vesicles to fuse with the presynaptic membrane, leading to the exocytosis of neurotransmitters into the synaptic cleft.
Therefore, a lack of extracellular Ca²⁺ would impede this process, resulting in a decrease in neurotransmitter release, not an increase.