A 12V 8Ah sealed lead acid battery is often chosen merely because it is the cheapest cost per capacity and tends to use use a simple/cheap charging circuit.
It could be very significant what you're trying to power with it, including needed duration (runtime), and "lithium" is just a chemistry family, not specific cells which will determine # of recharge cycles, pack voltage, and drilling down to particular cell construction and size, also max current.
So, there is no all around lithium equivalent. You could essentially ignore that the widget ever used a 12V, 8Ah and redesign a pack for what the widget needs including the discharge termination circuit and charge circuit.
Why not just use a 12V, 8Ah lead acid battery? If the size or weight is a factor, you will need to be all the more detailed in the minimum parameters the powered circuit needs instead of just overshooting it and getting the voltage "close enough".