Howdy.
If you're asking about your application that you've created in lazarus, you can save out the window positions (left, top, width, height) to a config file. Read the config file when the app launches and plug the config file values into the form's tRect.
If you're asking about the lazarus environment... I never got them to stick by way of lazarus configuration. You mentioned KDE, which is what I use, and there is a way to have KDE take care of saving window positions:
1) Right click on the title bar of the window.
2) Click Advanced -> Special Window Settings *
3) If needed, click the Geometry tab.
4) Enable Position and Size, selecting Remember from the drop down list.
5) Click Ok and repeat for each of the windows you'd like to have in the same spot.
* You can also try Special Application Settings but I never got it to work for all of the dialog/tool windows.
-Adam