Yes, lidocaine is well-known for being able to cause death if applied to "too much" of the body. Breaking the skin barrier (cuts, exfoliation) and plastic wrap keeping the topical spray on can greatly contribute to the overdose. The usual progression includes seizures, then respiratory arrest or heart attacks. This counts for tetracaine (more toxic), benzocaine, and prilocaine as well.
Interestingly, it can also cause the methemoglobinemia that is the mechanism of death in the ingestion of sodium nitrite.
I was able to find several suicide cases involving oral consumption of lidocaine. It is certainly a workable method of killing yourself, I just wouldn't be too excited about the seizures and possible heart attack. Death does appear to take a while.
I might keep it in my pocket as a backup method. It's certainly simple enough.