The failure modes are definitely a different style risk.
Lead's risk is more human-damaging, lithium's risk is more property damaging. (not that lead can't still destroy property, or lithium can't still hurt humans)
I've got a couple laptops, a half dozen old cell phones sitting in drawers, various wireless controllers/mice/keyboards etc all using lithium batteries sitting in my room right now, easily 20 I would imagine, and I don't think that's an abnormal number to have for a typical residence. While you do see/hear of fires starting from them on occasion, it seems to be pretty few and far between these days (unlike earlier more sketchy lithium cell designs from a decade ago).
I think a big part of the reason for that is the most common applications are largely single-cell, so good management of cell voltage is nearly effortless. That doesn't explain laptops very well though.
50million laptops were sold in 2011 in the US alone, and I would be willing to be only a tiny handful if any were sold that didn't use lithium batteries. I've not yet seen one that operates on just a single cell either (not saying they don't existor can't exist, but 3-5cells in series is the standard, and I've not personally seen below 3s yet). Out of a group of 50million, even a very small percentage that bursts into flames, say 0.0001%, that's still going to be 500 of them bursting into flames, and I don't think we're seeing that. 0.0001% for perspective is low enough odds that you're 10 times more likely to be killed in a motor vehicle accident.
I guess all I'm saying is, we can see that when setup and handled properly in a well designed system, lithium batteries are about as safe as anything involving energy/electricity/technology etc. I think the risk multiplies a LOT when we're not using anything like a properly handled well designed system though, like duct-tape batteries, sketchy BMS's with more sketchy install jobs, tab welds that wiggle and crack off randomly, wire routing that doesn't protect from chaffing related shorts etc etc.