No, you cannot connect lead acid and lithium batteries in parallel because they have different characteristics. To balance their voltage, you need a DC/DC converter.
If you connect two lead acid batteries together for loads only (somewhat difficult to achieve), the battery with the greater charge will try to charge the lower one. However, they will eventually stay equal but this will not last.
Check your battery chemistries – Sealed Lead Acid batteries for example have different charge points than flooded lead acid units. This means that if recharging the two together, some batteries will never fully charge. The result here would be sulfation of those that never reach a full state of charge, reducing their lifespan.
Lead acid batteries in solar systems die mainly because they are not charged adequately. This issue is more pronounced in large paralleled systems. In contrast, series string lead acid batteries have a mechanism that ensures 100% charge on all batteries by effectively overcharging some cells.
Normally we treat the cells in a 4 or higher voltage lead acid battery as a unit because the internal series connections usually makes them age, charge and discharge in a similar fashion because the usual limits of differences between cell (internal resistance) are usually smaller than the total load external resistance.
Series string lead acid batteries have a mechanism where each cell in the series sees the same voltage. This allows for 100% charge on all batteries by effectively overcharging some cells. The cells receive the same current.
What happens if you charge a rechargeable battery in parallel?
for secondary (rechargeable) batteries – the stronger battery would charge the weaker one, draining itself and wasting energy. If you connect rechargeable batteries in parallel and one is discharged while the others are charged – the charged batteries will attempt to charge the discharged battery.