Sure, this is possible. However, this author is not violating it.
For example, if the regular version were issued with the Pro version merged into it, the author would have to provide an unmodified version in the same distribution lest he violate the LGPL. There isn't much consequence to this, unless he felt the need to sue himself.
However, since the author here also owns the rights to both the regular and Pro versions, he can just license both to the user under a commercial license when including the Pro version, which is what he does. At that point, neither is 'free as in speech' from the perspective of the person who bought the license, even though lots of the bits are the same. The user is using a non-free commercial license. The user could also use the free version under the LGPL, but that would be redundant, since they have the same code under a license they can use from buying the commercial license.
In this case the author says he relicenses both for users who can't use LGPL code.
No, this is wrong. The author's code is licensed to the author under a "license" that allows him to do whatever he wants, since he owns the copyright.
Just because he chooses to extend the LGPL to others doesn't mean he is himself bound by its constraints.
In the model you're proposing (where things have one and only one set of copyright terms that apply to everyone), how would things like Libreoffice be offered under multiple licenses simultaneously?
For example, if the regular version were issued with the Pro version merged into it, the author would have to provide an unmodified version in the same distribution lest he violate the LGPL. There isn't much consequence to this, unless he felt the need to sue himself.
However, since the author here also owns the rights to both the regular and Pro versions, he can just license both to the user under a commercial license when including the Pro version, which is what he does. At that point, neither is 'free as in speech' from the perspective of the person who bought the license, even though lots of the bits are the same. The user is using a non-free commercial license. The user could also use the free version under the LGPL, but that would be redundant, since they have the same code under a license they can use from buying the commercial license.
In this case the author says he relicenses both for users who can't use LGPL code.