Drive backlight LCD led
No. You can't use the STLD41. (next time please supply a link or at least a complete part number, not all STM parts start with ST)

As the data on that part clearly states the maximum drive current is 120mA not the 700mA you need.
Taking a quick look at the other ST parts in that category none of them are suitable for a single high current string of LEDs. I think you'll need to look at a different manufacturer if you want a switching LED driver.

If you don't mind terrible efficiency you could use an LDO from the 12V rail in a constant current configuration. It would be simple but you'd be looking at >2W dissipated in the LDO so it'll get hot.