Choosing the grip width when doing lat pull-downs - does it matter? tl;dr: lat activation doesn't noticeably increase once you go wider than shoulder-width.
The lat pull-down is one of the most popular compound back exercises and it is a general belief that a wider grip activates the latissimus dorsi more than a narrow one, without any actual scientific support. In 2014 a study (1) published in the Journal of Strength and Conditioning Research found that 6 rep maximum strengths were higher with narrow and medium grip compared to wide grip.
There was similar EMG activation between grip widths for latissimus, trapezius, or infraspinatus, but a tendency for biceps brachii activation to be greater for medium vs. narrow when the entire movement was analyzed. Collectively, a medium grip may have some minor advantages over narrow and wide grips; however, athletes and others engaged in resistance training can generally expect similar muscle activation which in turn should result in similar hypertrophy gains with a grip width that is 1-2 times the biacromial (i.e. shoulder width) distance.
Reference: (1) Effects of grip width on muscle strength and activation in the lat pull-down. Andersen et al 2014