When converting the input into tokens (which is what TeX really works with) TeX will ignore spaces following a control word, that is, a control sequence starting with a backslash followed by letters, see Space after LaTeX commands
If you input
\rq\rq (the last character is a space)
there will be no space between the closing double quote and the parenthesis when you look at the printout.
You can obviate the problem in two ways
\rq\rq\ (the last character is a space)
\rq\rq{} (the last character is a space)
They have pros and cons. Look at the difference between
Donald said \lq\lq Good-bye.\rq\rq\ After that he left.
Donald said \lq\lq Good-bye.\rq\rq{} After that he left.

Do you see what happens? In the first case, the period is not considered as sentence ending, as it should. This is because \ (backslash space) resets the space factor to 1000, besides inserting a space. In the second case this doesn't happen, because {} doesn't influence the space factor.
Of course the input
Donald said ``Good-bye.'' After that he left.
doesn't suffer from the problem.
What's the difference between an explicit space (that survives tokenization) and \space? That the latter is a macro expanding to an explicit space. So you might do
Donald said \lq\lq Good-bye.\rq\rq\space After that he left.
and you'd get the same as with {}.
Note. Answers at the linked post about spaces after commands suggest \xspace: don't use it (besides, it isn't available in plain TeX).
...\rq\rq (...then the parenthesis would be attached to the right-quote. – campa Oct 26 '23 at 13:31\. – Y. zeng Oct 26 '23 at 13:33\, the space will no longer exist there. But is there a difference between space and\space? – Y. zeng Oct 26 '23 at 13:35\lq\lq I understandand\lq\lq\ I understand? – Mico Oct 26 '23 at 13:36:-)Keep reading! – campa Oct 26 '23 at 13:37\" tells TeX to, well, insert a space. – Mico Oct 26 '23 at 13:39\lq\lq I understand.\rq\rq\, so there are always a whitespace between the quotation characters and the word "I". – Y. zeng Oct 27 '23 at 10:43\lq\lq) and the word "I" only if you change\lq\lq I understandto either\lq\lq\ I understandor\lq\lq\space I understand. – Mico Oct 27 '23 at 11:30