Counting consecutive selections of a given number when sampling integers in a range
You can use the itertools for this.

Just groupby the value to get groups of equal values, filter for the desired value, then get the length of each streak and finally take the max of that length:

from itertools import groupby

def longest_streak(values, desired_value):
    return max(len(list(group))
               for value, group in groupby(values)
               if value == desired_value)


(I think it should be streak, 4. b: "an uninterrupted series" and not strike.)

Then your main can code become this:

from random import randint

if __name__ == "__main__":
    desired_number = int(input("Desired number: "))
    lower_range = int(input("Lower range: "))
    upper_range = int(input("Upper range: "))
    iterations = int(input("Iterations: "))

    numbers = (randint(lower_range, upper_range) for _ in range(iterations))
    print("Biggest consecutive strike: ", longest_streak(numbers, desired_number))


Here numbers is a generator, so the function can just consume the numbers as they are generated (meaning that this will occupy at most len(group) space in memory). 

if __name__ == "__main__": is a guard so that the code under it is only executed when directly executing this script, but not when importing from it.