I have two threads running. They share an array. One of the threads adds new elements to the array (and removes them) and the other uses this array (read operations only).
To answer your question: maybe.
Simply put, the way that the question is framed doesn't provide enough information about whether or not a lock is required.
In most standard use cases, the answer would be yes. And most of the answers here are covering that case pretty well.
I'll cover the other case.
When would you not need a lock given the information you have provided?
There are some other questions here that would help better define whether you need a lock, whether you can use a lock-free synchronization method, or whether or not you can get away with no explicit synchronization.
Will writing data ever be non-atomic? Meaning, will writing data ever result in "torn data"? If your data is a single 32 bit value on an x86 system, and your data is aligned, then you would have a case where writing your data is already atomic. It's safe to assume that if your data is of any size larger than the size of a pointer (4 bytes on x86, 8 on x64), then your writes cannot be atomic without a lock.
Will the size of your array ever change in a way that requires reallocation? If your reader is walking through your data, will the data suddenly be "gone" (memory has been "delete"d)? Unless your reader takes this into account (unlikely), you'll need a lock if reallocation is possible.
When you write data to your array, is it ok if the reader "sees" old data?
If your data can be written atomically, your array won't suddenly not be there, and it's ok for the reader to see old data... then you won't need a lock. Even with those conditions being met, it would be appropriate to use the built in atomic functions for reading and storing. But, that's a case where you wouldn't need a lock :)
Probably safest to use a lock since you were unsure enough to ask this question. But, if you want to play around with the edge case of where you don't need a lock... there you go :)