Is it somehow possible do get the desired result without any graphical workaround.
No. Not as far as I know.
I think you could create an invisible syllable with a hard space below the half note and activate the extension line via the properties panel. (Not sure because I’m not in front of Dorico now.)
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Checking in after 5 years, since I bumped into that situation, too, and wonder, if there is a different solution now available?
Since extenders do not normally extend under single (untied) notes, adding a hard space under the dotted half note in measure 21 would probably not produce an extender without additional manipulation.
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Unfortunately, no, we have not yet tackled the complex area of handling notations that are split by repeats. It is of course on our backlog of things to develop in future.
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The usual workaround is to use an LV tie, and then move it to the other side of the note.
As Derrek points out, a lyric extension only goes to the right-hand end of the last note (and certainly not to some mid-way point within the note’s duration! 
).
But for other situations, you could perhaps use the Line tool.
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Yes !
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