LM317 Constant Current Battery Charger Question
Figure 1. Line regulation for the TI LM317 indicates that it could require 3 V headroom to operate properly.

The LM317 has a relatively high dropout voltage compared with modern LDO (low drop-out) regulators. Add to this the 1.25 V across the current sense resistor and you can see that your supply voltage is too low.

The big question is why you are charging lead acid batteries using constant current. You should be using constant voltage.



From the datasheet:

9.3.8 50-mA Constant-Current Battery-Charger Circuit

The current limit operation mode can be used to trickle charge a battery
at a fixed current.
\$ I_{CHG} = 1.25V ÷ 24Ω \$. 
\$ V_I \$ should be greater than \$ V_{BAT} + 4.25 V \$. (1.25V [\$ V_{REF} \$]+
3V [headroom]).