Can my friend's LCD tv display 1080i WITHOUT the cable HD receiver in the line?

If his TV has a digital tuner (QAM), then he will likely get some digital HD channels. More than likely this will be limited to the same stations he can get with an OTA antenna, but may be numbered differently. The other cable channels will be 480i. That is certainly how Comcast does it. In fact, if he hooks up a standard cable box, he will be blocking the HD stations he can receive now.

Like dnoyeB said, connecting the cable from the wall, without any cablebox, will allow him to autoprogram/scan for channels with the TV's internal digital QAM tuner. I have a Samsung LN52A860 and have done that. Comcast gives us all the local channels in HD and a few other cable channels in SD.

If for example, NBC in your area has always been on channel 4, an NBC SD broadcast will be available on 4, while NBCHD will be available on 4-1. Likewise, CBS has always been 62 in our area and CBSHD comes in on 62-1. PBS is 56-1. When you tune in these stations, use the info button on the Samsung remote to verify that they are in 1080i. ABC comes in on 7-1 and is 720p.

It also appears there is a set of local channels in HD up around 400 or 700, but they seem to be just stretched SD versions of the broadcasts.

Finally, if you connect a non-HD cablebox to the wall cable and then to the TV, it will block those HD stations from coming in. If you connect, say a Comcast HD box, ABCHD will come in on 231, NBCHD on 232, etc., plus almost all cable stations have HD broadcasts now, e.g. ESPNHD, TNTHD, etc.

To use your example dfp, in my area channel 4 analog/SD will not be on 4-1. The '-' channels are all original source digital. So typically 4-1 will be the HD channel. 4-2 will be an alternate digital channel. The analog/SD station will be the one up around 400. Though it typically shares the same programming as the HD version.