I've found an old lead-acid battery and decided to check if it still is in a decent condition. I've opened all rubber caps and checked that the water level was still OK. It measured 10.5 V before I started charging.
I programmed a controllable power source to provide 13.15 V under a 1.4 A current limit. Differently from what I expected, charging current started at about 100 mA (constant voltage) and it's slowly increasing for 2 hours. It has just passed 600 mA.
The battery is not heating or noticeably releasing gases.
Is this expected? It's different from the behavior we normally see on deeply discharged batteries (current limited first, than constant voltage).