If you repair LCD Monitor and confirmed that the backlight (lamp) was the caused of the problem then your next steps would be either replace the bad backlight with a new lamp or salvage from a used LCD Monitor. The questions is whether one could use a replacement backlight from other brand? The answer is Yes, if the backlight could fit into the original location. For your information, backlights comes in different diameter and length. Use a 15″ backlight to replace into a 15″ LCD Monitor and you can’t use it to put into a 17″ LCD Monitor as it would cause the edge to be slightly dim and may have imbalance brightness! Choose the one that have the same diameter as a bigger diameter may cause the backlight can’t be fitted into the original location.
As for the backlight connector, you can always use back the original backlight connector to joint into the replacement backlight (assuming the replacement backlight have different connector). If you don’t have a new backlight then it is wise to keep some used LCD Monitor for future use like comparison/troubleshooting and replacement purposes.