Can you\why don't some restuarants marinade without chicken skin? I bought some grilled chicken from a restuarant and it came with marinade on the skin.

I asked the seller if they can provide grilled skinless with marinade on flesh.  He said we don't do it like that because the marinade doesn't go well on the chicken flesh.  I also notice other shops dont marinade without skin.

However I have previously bought lamb chops from the same restuarant and it has been well marinated.

My thinking is, if you can marinade and oven grill lamb chops then you can grill chicken too with marinade to a similar effect?

What did he mean, is there a reason why restaurants may marinade meat but not skinless chicken meat?
There's an overlap, and a difference, between a marinade and a glaze. If a mixture contains a fair amount of sugar, then it's probably intended more as a glaze, and the cooking method will usually be grilling, or roasting, (rather than pan frying). There's no reason not to glaze poultry flesh directly (teriyaki, for example) but the bigger the piece, the longer the  exposure to fierce heat will have to be to cook it to the middle. It's not easy to grill a whole skinless chicken breast without drying the outside before the middle is cooked. The combination of the fat from the skin and a glaze will protect and baste the flesh. The surface will be crisp, juicy, and caramelized, rather than parched and leathery.