We submitted to peer-review journal that has several Associate Editors. One of them is a lecturer in our department. Thus, the editor will not assign our paper review to him/her. Do we understand correctly?
Yes. An editor from the same institution as the authors has a clear conflict of interest, which is to be avoided.
I focus the following primarily on the review aspect, not on the editorial aspect.
I think the correct answer to this is that it is very unlikely, but not impossible. But background is needed. The main issue is conflict of interest. There are three parties and their interests partly align and partly not.
The journal, and the senior editor acting in its name, has an interest in publishing good papers (leaving out predatory journals here). The associate editor, under the senior editor, has the same interest.
The author has an interest in publishing papers, preferably good papers, but, for some, any paper will do. This is where the alignment of interest isn't perfect.
The reviewer has an interest in improving any paper and in providing good advice to the journal (editor).
However, in a case such as that presented by the OP, there is, possibly an additional interest of the reviewer, but we don't know what that is, since we don't know the nature of the relationship between the reviewer and author other than that they have the same employer. The relationship might be friendly/supportive, or it might be poisonous. Or, it might be anything in between.
But if we consider the situation of the senior editor and the associate, it is possible to know something of the nature of the relationship before any assignment is made, since, we hope, they work together and have a trust relationship.
Note, however, that reputations are involved, and, in fact, a reviewer's reputation (with the journal, at least) is harmed by giving improper reviews for any reason, including just laziness. So a reviewer has an additional interest in being fair and accurate. But this may not be their strongest motivation, of course. The editor's reputation, however, is much more affected by the outcome. I don't think an editor would last long by publishing bad papers or by making enemies of authors. An editor's academic reputation, in the current case, would certainly be harmed by improper actions if/when brought to light.
The editor, knowing all of this (we hope), but most likely not knowing anything of the relationship between reviewer and author, will be (should be) cautious. Hence, the unlikelihood that this reviewer will be assigned even in the face of the known alignment of interest otherwise. But the situation between senior and associate editors, involves more knowledge, at least in theory.
As an aside, the reason we have reviewers is that authors are often poor judges of their own recent work. If that were not true, review would be less necessary, though improvement is always good.
However, I can see situations in which an editor has a long term relationship with a reviewer and trusts the reviewer to do the right thing regardless of other circumstances. I've known of such situations in which an editor leans heavily on a certain trusted reviewer. This is, I think, unlikely in the case at hand, but cannot be ruled out entirely. Hence, I conclude that this reviewer might be assigned. Of course s/he might validly refuse. And, exactly the same situation applies between a senior editor and an associate.
Note that in a double blind review, none of the complications arise if only the senior editor knows the identity of all parties.