Lead acid batteries suck for more reasons than just their size and weight. One major disadvantage is that the faster you discharge them the less of their charge you will actually recover[1]. Additionally, discharging them below 50% capacity significantly reduces their life in terms of total cycles (even for cells rated for "deep cycle" operation)[2][3] so you need to oversize your battery system to get the same effective capacity if you want your cells to last. Lithium batteries suffer from neither of those drawbacks.
If those weren't enough, even when treated well (not discharged too deeply) lead-acid batteries don't last for as many discharge cycles as lithium iron phosphate cells. If you do the math, for batteries cycled daily modern LiFePo batteries are about the same TCO as lead-acid despite the higher up-front costs because the lithium batteries will last significantly longer and you don't need to buy as much absolute capacity for the same effective capacity. Here's a good presentation on this: https://www.youtube.com/watch?v=BRqRDZh74F0
If those weren't enough, even when treated well (not discharged too deeply) lead-acid batteries don't last for as many discharge cycles as lithium iron phosphate cells. If you do the math, for batteries cycled daily modern LiFePo batteries are about the same TCO as lead-acid despite the higher up-front costs because the lithium batteries will last significantly longer and you don't need to buy as much absolute capacity for the same effective capacity. Here's a good presentation on this: https://www.youtube.com/watch?v=BRqRDZh74F0
[1] http://omahamakergroup.org/2015/05/14/battery-derating-and-c...
[2] https://www.pveducation.org/pvcdrom/lead-acid-batteries/char...
[3] https://www.solar-electric.com/media/wysiwyg/cyclelife2.gif (Graph shows cycles (y-axis) vs average depth of discharge (x-axis) for a typical "deep cycle" lead-acid battery. Note the y-axis is logarithmic.)