Dealer is always advisable, if you dont know much like what interval service has what all things to be changed and all.
However in shj there are plenty american car specialist behind BM road, back side of alico. Make a visit and educate yourself and choose any as per their confidence and explanations.
In dubai there are few like
Salim Ali Bin Haider Garage in umm ramool you can call Mr. Rizwan Ali at 050-5350770
Radiant Car Workshop in Umm Ramool 04-2863836
Or robbies motorsport in al quoz, just find there number from yellow pages
Dubai will be slightly costly than shj but more professional too. Better is buy ur original parts from dealer in shj/dubai at discounted rates and get service wherever you are fine, so you be sure that Lumina SS type of beast will be happy and healthy with original lubes and parts.
Parts guys
Abdulla Abdul Wahed Motor Spare Parts 04 2950238
Alsafa Trading 04 2235740
Binduman Auto Parts 06 5420093