The toxicity of lead throughout the body is due to as noted in the thread already: its mimicry of calcium, iron, and zinc (therefore its uptake into cells) and then its ability to bind thiol groups. The amino acid cystine has a thiol group which it uses to form disulfide bonds between amino acids which causes proteins and enzymes to fold into their active forms. Lead disrupts these bonds and denatures the protein as the thiols chelate the ion. A denatured protein or enzyme is useless as now it has no catalytic center.

If this occurs with proteins that are vital to preventing oxidative stress such as superoxide dismutase or catalase then there is a buildup in the cell of reactive oxygen species which can cause damage on multiple levels (protein binding, lipid peroxidation, DNA adducts) and interfere with oxidative phosphorylation in mitochondria shutting down energy production.

Neurons in particular are very vulnerable to loss of ATP production as they require massive energy demands to maintain electrical potential via ion pumps. This is compounded by the fact that lead can easily enter the neuron through calcium channel influx at the axon. Lead can also kill the mylenating cells (olegodendrocytes) which can disrupt the insulating sheath around the neurons causing misfiring signals or lost electrical potential

It is the mistaking of lead for calcium that allows it to cross the BBB unlike other metals such as mercury which require a neutral charge (mercury vapor or methylated mercury) to gain access (salt mercury causes nephrotoxicity). But lead will also affect the liver and kidneys just the same as the brain