Will this docking station charge the ThinkPad E580 using it?

Yes, this docking station supports upstream USB-C power delivery specification revision 3.0 and can provide up to 65W power supply, which should be sufficient to charge the ThinkPad E580.

Questions & Answers: Wavlink USB-C Triple Display ( Dual DP + 1 HDMI) Docking Station with 65W Charging, USB C Gen 2 System, 2 Display Ports & HDMI, 4 USB 3.0, SD/TF Card Reader, Gigabit Ethernet) For MacBook Pro, Windows

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Wavlink USB-C Triple Display ( Dual DP + 1 HDMI) Docking Station with 65W Charging, USB C Gen 2 System, 2 Display Ports & HDMI, 4 USB 3.0, SD/TF Card Reader, Gigabit Ethernet) For MacBook Pro, Windows

13 in 1 Docking Station - USB-C PD charging port, Gigabit RJ45 Port, 2 x 4K DP ports, HDMI port, SD/TF Card Reader, 4 x super speed USB 3.0 ports(Up to 5Gbps) for one port with fast charging, 4-Pole Phone Jack. Plug and play, no driver needs.
Triple Display - Supports to connect up to 3 monitors. Resolution up to 3840x2160@60Hz when single disply. Resolution up to 2560x1440@60Hz with dual displays attached. Resolution up to 1920x1080@60Hz in triple display.
Power Delivery - The upstream USB-C port is compliant with USB power delivery specification revision 3.0 and supports up to 65W power supply. One of USB 3.0 Type-A ports supports BC 1.2 fast charging to USB-A devices.
Data Transmission - Four USB 3.0 Type-A ports for super transfer speed up to 5Gbps, build in Combo SD / TF Card Reader SD V3.01 support SDHC / SDXC capacity up to 2TB, you can connect different external USB devices and do high-speed file transfer when working.

$94^.99 –