Is it correct to use LOCK TABLES READ to preserve data integrity in this case?

Question

PHP

A topic is created and a message is added to the topic. The parent of the message is the number of the newly created topic:

mysqli_query("LOCK TABLES `themes_table` READ;"); 

mysqli_query( "INSERT INTO `themes_table` ( ... ;" );

$new_theme_id = mysqli_insert_id();

mysqli_query( "INSERT INTO `posts_table` ( `parent_theme_id`=$new_theme_id, ... ;" );

mysqli_query("UNLOCK TABLES;");

I want to avoid the case when, before inserting the message, another process creates a topic and the insert_id is incorrect. Do I understand correctly that after a LOCK TABLES `themes_table` READ lock, another process will not be able to write a new theme to `themes_table` until that process UNLOCK TABLES?

Answer 1

insert_id will be wrong

Impossible. For any recording intensity. The value of last insert id is session value, not global value.
Wrap it in a transaction - then no one will see the partially recorded transaction until the commit. If we talk about transactional things, of course, and not some myisam.

Answer 2

Is mysqli_insert_id(); will return not the same id that was created in the current connection? And then the hypothetical other connection will not affect it in any way.