Rather than me mucking about with reinventing the wheel, see if these are usable:
https://github.com/mkottman/lqtClick on "Downloads", he has prebuilt binaries for Qt 4.7 there. Not 4.7.1 tho, but they should be ABI compatible.
I'll be testing myself, and if they work OK I'll ship some of them with LCDHost.
Note that any GUI calls from Lua will fail, since only the main thread may do GUI calls with Qt.
The following libs *should* be mostly safe though:
qtcore.dll
qtnetwork.dll
qtxml.dll
qtxmlpatterns.dll
QtCore especially should be interesting to you, as that binds QString with it's excellent conversion methods and QRegEx.
Come to think of it, if these bindings are of high enough quality, perhaps QImage and QPainter is a better bet than Cairo for rendering.
Those would be in qtgui.dll.
EDIT again: Well, doing require "qtgui" causes a crash, so replacing lcairo isn't going to happen. But QString seems to work fine.