Lani Wall Fan
 

I have a small lani that I had enclosed with thermal pane windows and lani ceiling insulated. We keep the sliding door open to maintain a comfortable temperature in the lani. I would like to move more of the temperature controlled house air into the lanai with a wall fan. Has anyone had experience installing a wall fan through an internal wall and through an external stucco block lani wall? If so any issues?

You do not mention the type of construction of your house, stick, concrete block, poured concrete, etc. In any case locating the fan in the area of the slider may be problematic, also areas to either side may have 120 VAC wiring, I know ours does. Concrete block walls are thick and there are locations that are solid concrete with steel rebar installed.
I would suggest an oscillation floor fan close to the slider opening I have seen many models some with remote controls.

Since you insulated and thermopane glass any A/C company could install ductwork to extend A/C into lanai.

Not true, check building codes, the AC company would need to report the work and then there maybe tax implications. Be very careful on this option.