**Core Concept**
Local anaesthetics are a class of drugs that temporarily block nerve conduction by inhibiting the generation and transmission of action potentials in neurons. The speed of onset of action of local anaesthetics is influenced by their pharmacokinetic properties, particularly their lipid solubility and protein binding.

**Why the Correct Answer is Right**
The speed of onset of action of local anaesthetics is primarily determined by their ability to rapidly penetrate the neuronal membrane and bind to sodium channels. Local anaesthetics with higher lipid solubility, such as lidocaine and mepivacaine, can more easily penetrate the lipid bilayer of the neuronal membrane, resulting in a faster onset of action. In contrast, local anaesthetics with lower lipid solubility, such as bupivacaine and ropivacaine, have a slower onset of action due to their reduced ability to penetrate the membrane.

**Why Each Wrong Option is Incorrect**
**Option B:** This option is incorrect because the duration of action of local anaesthetics, rather than their speed of onset, is primarily determined by their protein binding and metabolism.

**Option C:** This option is incorrect because the potency of local anaesthetics, rather than their speed of onset, is primarily determined by their ability to bind to sodium channels and inhibit action potential generation.

**Option D:** This option is incorrect because the systemic toxicity of local anaesthetics, rather than their speed of onset, is primarily determined by their ability to cross the blood-brain barrier and bind to sodium channels in the central nervous system.

**Clinical Pearl / High-Yield Fact**
A mnemonic to remember the factors influencing the speed of onset of local anaesthetics is: "LIPID" - Lipid solubility, Ionization, Protein binding, Intravascular concentration, and Diffusion.

**Correct Answer: A. Lipid solubility.**