Questions regarding Lock Objects.

I am creating a custom table and I want to implement a unique ID for my table and I want to use the technique of auto-increment. I created a seperate table where to store the increments to be used as IDs. So basically, when a new data is going to be saved on my other table, the program will query the next "id" from the table for increments. I have to make sure that the updating and reading of the data from the table is accessed one at a time to rule out the possibility that there will be no duplicate IDs generated.

I have read about shared locks and exclusive locks which would serve as a solution for my purpose. The question is: is it possible for other users to "read" from a table if it is currently in an "exclusive lock" by another user?