A memo shouldn't give any problem with a meagre 7K lines.
ShowMessage, though, is meant to show a relatively short text and not only is it quite limited but depends heavily on the facilities of the window or composition manager.
In this machine, for example, a 64KiB message is about the limit, and the window occupies almost the whole screen; a few more lines and not only crashes the application, but also Metacity (the composition/theme manager) itself. It might be due to a buffer overflow, overflows when calculating the size and/or position of the messsage window, or a miriad other things, but the underlying reason is that the widget isn't meant for that.
If you really need to show such a big message you'd better write your own message dialog using controls (like TMemo) able to handle such quantities of text.