Many X applications assume that the screen size is at least 1024x768 for historical reasons. I cannot advise you for other programs but for GNU Emacs the solution is simple.
Add this line
(when window-system (set-frame-size (selected-frame) 80 24))
to you ~/.emacs file with values suitable for you.
BTW, Emacs behaves differently on Gnome where it fit nicely even on smaller screen sizes.
As for other applications, you might just have to move the window with your mouse with the "alt" key pressed.
You can also increase the size of you logical screen with command such as:
xrandr --fb 1680x1050 \
--output LVDS1 \
--scale 1x1 \
--panning 1680x1050/1680x1050+0+0/100/100/100/100
again substituting your own sizes and display device.
Sometimes I might scale my 1024x800 notebook screen to accommodate programes requiring a larger screen:
xrandr --fb 1280x750 \
--output LVDS1 \
--scale 1.25x1.25 \
--panning 1280x750
(Actually those are snippets of my "disp" script which lets me handle my screen with various ways.)
I don't know whether this xrandr thing works on LXDE but it surely works on Gnome.