How does a lead acid battery accept more current when it is discharged than when it is charged if the resistance is higher when it is discharged?
Not everything has to follow Ohm's law because not everything is a resistor. A battery is not a resistor. It is a battery. A typical beginner mistake when they first learn Ohm's Law is that they think everything follows Ohm's Law. I don't know why since it is clearly taught that Ohm's Law is for resistors, but I guess when the only tool you have is a hammer, everything looks like a nail.
Consider this: when a battery is discharged the internal battery voltage is lower, meaning there is a larger voltage difference between the battery voltage and the charging voltage. More voltage difference = more current. If that voltage difference is large enough the resulting increase in current can offset the decrease in current due to the higher resistance.