iPad connected to LG Ultrafine 4K Display
No, it will only charge the iPad.

Lightning doesn't have anything to do with HDMI. It's just a serial bus that cannot send any HDMI data without some help.

With Apple's Lightning Digital AV Adapter (which, in fact, is just small computer itself) you can output to an HDMI display. The native resolution is only 1600x900, however.