When does LH surge actually occur?
Some graphs about the ovarian cycle mention only the follicular phase and luteal phase, and the ovulation just as a point in time, not a phase, for example, here:



Source: Differencebetween.com

In this case, the LH surge starts in the follicular phase and peaks at ovulation or shortly before it.

Some other graphs also show the "periovulatory" phase (or "ovulatory phase" or just "ovulation" as a phase):



Source: Nature - Scientific Reports

In this graph, LH surge starts few days before ovulation, so in the follicular phase and peaks in periovulatory phase. 


  The first half of the menstrual cycle is comprised by the menstrual
  and follicular phases during which time estrogen levels are low
  (menstrual phase) and rise (follicular phase) and ends with the
  periovulatory phase in which follicular stimulating hormone (FSH) and
  luteinizing hormones (LH) peak.


Now, these graphs are still confusing, but Merck Manual defines the ovulatory phase by the surge of LH and FSH:


  The ovulatory phase begins with a surge in luteinizing hormone and
  follicle-stimulating hormone levels.


In conclusion, LH surge occurs in the ovulatory phase, if the source mentions it as a separate phase, and if not, it occurs in the follicular phase.