A small add at this seems to be some confusion here.
Either if a Always on setup will be recommend based on your volumes, a MSSQL cluster will not prevent a lock when the index is been rebuild. This will only help to speed up the rebuild itself making a lock more unlikely.
The best way to handle this is to not wait that your index been too much fragmented before reindexing. You dba must monitor the grow of the defragmentation and identify the pattern.
Based on that pattern identified, schedule a periodic reindexing for those. Then the operation will take less time to complete
This is also important to split your jobs for reindexing across the time meaning make sure that you don't rebuild all your index on all you table at same time but identify the one consuming and scheduled those separately
Make sure you DBA is using online index rebuild vs.offline. (assuming you have an SQL enterprise)
Online will only lock twice during a online reindexing of a table at start and the end of the index and this is really short.
Therefor you may want also to strongly look at the overall performance of you DB server and do the necessary action to optimize.
A bottleneck for indexing been mostly I/O performance (make sure your infra can support I/O at top speed, more specially if you run your SQL server on VM where latency will be higher)
Note also that an important contributor of fragmentation is free space in your database.
First the auto growth of your DB must never use % in your setting but directly MB.
Depending of your growth make sure that put enough there. at the price of HDD today don't hesitate to put 100 mb or more there for both the mdb and mdb (look at the actual size of you mdb and mdb_log and ensure that amount there correspond at less to 10% of the size)
If you own MSSQL 2014 or higher you can also take advantage of the Managed Lock Priority that was introduced there.
You will then be able to define a low priority for the ALTER INDEX.
There is a nice article there on it:
https://www.sqlshack.com/control-online-index-rebuild-locking-using-sql-server-2014-managed-lock-priority/
DBA staff and responsibility but hope this help your conversation with him.
My 2cents
/J