The problem is likely to be that you need to adjust the tension on the gear cable. Do this with the barrel adjuster where the cable enters the rear dérailleur. If the lag is when you change up to a harder gear your need to turn the adjuster clockwise - not too much, proceed in quarter turns while turning the cranks and shifting the gears. It's easiest if you have a work stand, but you can do it perfectly well with the bike upside down.

If you are struggling to follow this explanation, simply google for " adjusting a rear dérailleur". There's a ton of videos on YouTube. It couldn't be easier, no need for a mechanic.