not phrasing the question specifically enough.... How would the linkappend tags be positioned in this case?
That is a whole different nightmare, which you can't solve using the <<linkappend>> macro because it is designed to append the 'additional text' directly after the 'Link Text', and you want that 'addition text' appended to the end of line containing the link.
NOTE: The following solution is just one a number of implementations you could use, each one is just as messy as the other because the effect you're asking for (a Jonah type endless-page layout) isn't as easy to implement as you may think.
Without creating your own custom set of macros I believe you will need to use the <<linkreplace>> macro and the <<append>> macro to achieve what you want, and even then the implementation will be very messy.
1. Create a target for your <<append>> macros using an ID'ed Custom Style.
This target can also contain your first line of text and first <<linkreplace>> macro, which will use the <<include>> macro to inject the TwineScript for displaying the 2nd line of text and link.
The <<linkreplace "quick">><<include "Line 2">><</linkreplace>> brown fox
2. The Line 2 Passage is used to inject the 2nd line of text.
This passage first overwrites the 1st link's Link Text, it then uses an <<append>> macro to add the 2nd line of text containing the 2nd link. The second link uses an <<include>> macro like the 1st link did.
\ <<linkreplace "over">><<include "Final Line">><</linkreplace>>
3. The Final Line Passage is used to inject the 3rd and final line of text.
This passage basic works the same way as the previous one did.
<<append "#output">><br>the lazy dog.<</append>>
The more lines of text (containing a link) you want the more copies of the Line 2 passage you will need, and each of those passages will need a unique name.