Yes. Lantus (insulin glargine) can cause hypoglycemia, or low blood sugar. It is a long-acting insulin, so low glucose can occur hours after the injection and may last longer than with shorter-acting insulin.
Common symptoms include shakiness, sweating, hunger, fast heartbeat, headache, dizziness, irritability, confusion, blurred vision, or weakness. The FDA labeling identifies hypoglycemia as the most common adverse effect of insulin, including Lantus.
FDA prescribing information
Do not stop or change Lantus doses without contacting your prescriber, but recurrent lows need a prompt dose and regimen review.