MySQL does not have this feature. For anyone searching for this topic in general, some RDBMS have better/smarter locking features than others.
For developers constrained to MySQL, the best approach is to add a column (or use an existing, e.g., status column) that can be set to "locked" or "in progress" or similar, execute a SELECT ID, * ... WHERE IN_PROGRESS != 1 FOR UPDATE;
to get the row ID you want to lock, issue UPDATE .. SET IN_PROGRESS = 1 WHERE ID = XX
to unlock the records.
Using LOCK IN SHARE MODE
is almost never the solution because while it'll let you read the old value, but the old value is in the process of being updated so unless you are performing a non-atomic task, there's no point in even looking at that record.
Better* RDBMS recognize this pattern (select one row to work on and lock it, work on it, unlock it) and provide a smarter approach that lets you only search unlocked records. For example, PostgreSQL 9.5+ provide SELECT ... SKIP LOCKED
which only selects from within the unlocked subset of rows matching the query. That lets you obtain an exclusive lock on a row, service that record to completion, then update & unlock the record in question without having to block other threads/consumers from being able to work independent of yourself.
*Here "better" means from the perspective of atomic updates, multi-consumer architecture, etc. and not necessarily "better designed" or "overall better." Not trying to start a flamewar here.