Explanation
No. Lightning can strike the same place more than once. A previous strike does not prevent another discharge from reaching that location.
NOAA's National Severe Storms Laboratory explicitly confirms repeated strikes. The UK's Met Office independently describes the same phenomenon, citing repeated strikes to the Empire State Building.
Height helps explain why some structures are struck repeatedly. NOAA explains that taller objects are more likely to produce an upward electrical channel that connects with a developing flash. This makes repeat strikes physically understandable, although lightning does not always hit the tallest object.
Key takeaway
A lightning strike does not make a location immune to future strikes.