Rory helps Henry organise a three-way or party line conversation so that Lane and Henry can talk, while Mrs Kim believes that Lane is talking to Rory. It was done by calling the first person, then pressing the FLASH button before dialling the next person then pressing FLASH again. It cost extra and showed up on the phone bill. It’s still possible to do on a landline today, as well as a mobile phone.
This is the first thing Rory has done to help Lane and Henry, and it’s pretty minimal. Lorelai seems to be aware of the deception towards Mrs Kim, but doesn’t feel any need to tell her the truth despite her supposed “mom code”. Henry met Lane eight months ago, and must be very keen to be kept interested with occasional five minute phone calls, conducted with some difficulty.