LCD panels use different connectors, and for some projects, you might need to source the connectors, plugs or contact. Here, I'll gradually assemble information about part numbers, as I either find it or someone else shares it. If you cannot find it here, mind that often connector information is found in your LCD's datasheet, or a datasheet of an LCD with the same connector. If you find information that isn't present here, please leave it in the comment section below!

FI-X 30-pin connectors for CCFL LVDS

These tend to be JAE FI-X series connectors. Such connectors are found on cables like FIX-30P-D6 and FIX-30P-S6, typically used for CCFL-backlight LVDS LCDs. Contact housing (plug) is called FI-X30H (HL for the locking version), individual contacts can be found as FI-XC3A-1-15000 and mating parts can be found as FI-XB30SSLA-HF15, FI-XB30SSRLA-HF16, FI-X30SSLA-HF, FI-X30SSLA-HF-R2500 - there might be more, but they all should be described on the page linked right above. On Aliexpress, FI-X30SSLA-HF-R2500 has given particularly good results for sourcing SMD connectors themselves.

Thanks to @helge to sharing this!

40-pin and 30-pin LVDS-LED and eDP connectors

The 40-pin version

These connectors tend to be used for both LVDS LED-enabled and eDP screens (30-pin for common ones, 40-pin for high-res or touch-enabled screens). The original part number seems to be I-PEX 20455-030 and I-PEX 20455-040, and the 30-pin and 40-pin SMD sockets are found on LCSC as JUSHUO ALC04-S30EIA-00 and ALC04-S40EIA-00 respectively. I searched for "LVDS" in the search bar to find these. Hopefully, that helps.