Running 2560x1080 on LG 29UM57-P on an old MacBook Pro OSX El Capitan

Yes. A mid-2011 MacBook Pro running OSX El Capitan can drive a 2560x1080 monitor via HDMI.

I was not able to get 60 Hz working. I am settling with 53 Hz. I tried many settings before finding something that works. The refresh rate seems fine to me. Maybe the text could be clearer but for a $200 monitor running this resolution, I'll take it. Apple MacBook 2015 retina resolution is 2560 x 1800. Consider buying a better monitor that may literally give you fewer headaches.

1. Install SwitchResX
2. Follow the instructions for disabling SIP
3. After rebooting, run SwitchResX via System Preferences
4. Select your LG monitor
5. Click Custom Resolutions
6. Click the + icon 
7. Enter these settings (source)
8. Exit SwitchResX and save
9. Reboot
10. Run SwitchResX via System Preferences
11. Select your LG monitor
12. Click Current Resolutions
13. Select the 2560x1080, 53 Hz setting
14. Enable SIP

If you discover better settings, please leave a comment.