Concurrently update with limit mysql
This depends on table engine?


Yup. MyISAM will lock the table, InnoDB will lock rows

If you're looking for ACIDity, you'll want to be using InnoDB. How InnoDB handles locking is described in this doc page

The following user comments on the above document page illustrate a flaw in InnoDB performance on large tables:


  Major gotcha: Rows are locked during updates using indexes. For example, UPDATE tab SET col1=3 WHERE col2=17; will lock the entire table unless col2 is indexed (in which case, only rows where col2=17 will be locked).


and


  To expand on the above comment, any operation that does a table scan for update/delete will lock all the rows in the table


Extra curricular reading: 


  TL;DR: InnoDB index lock is major architectural performance flaw, and that is why you hear that large tables are slower. There’s a big chance that there’re more scalable engines for on-disk writes out there, and all the large InnoDB write/insert benchmarks were severely hit by this.