Because Lantus insulin (insulin glargine) is dissolved in an acidic liquid with a pH of 4 in the pen, when it is injected under the skin it can sting. Injecting any acid would be similar but fortunately this discomfort only lasts a short while. Once injected the pH quickly neutralises.
Lantus may also sting if the amount of insulin injected is large in volume or if the insulin is injected into the skin itself rather than under the skin. This would result in a lump in the skin where insulin was injected. If using a 4mm needle sometimes changing to a 5mm needle may help reduce any stinging sensation.