Thanks for reaching out to us, I am happy to help!
We have not specifically tested the Lenovo Yoga 730 with our docking stations, however based on the Lenovo product descriptions, both the 13" and 15" models should support at least one display on the Thunderbolt 3 port as well as host charging. While Thunderbolt 3 is physically capable of supporting up to two 4K displays, the Lenovo Yoga 700 line ( both the 710 and 720 ) only have supported one display and Lenovo documentation does not provide any concrete details either direction. With this a hybrid hardware connection and software assigned solution can support bot of these displays however may have reduced performance on one of the displays.
Based on your description, our USB-C Triple 4K Display Docking Station with Host Charging UD-ULTC4K ( https://plugable.com/products/ud-ultc4k ) may be a good fit. This docking station connects one monitor directly to the internal graphics controller using Type-C DisplayPort Alternate mode allowing for up to 4K resolution at 30Hz refresh rate ( or up to 1440P, 2560x1440 resolution at 60Hz ). Two additional displays DisplayLink based USB indirect graphics output support up to 4K UHD ( 3840x2160 ) at 60Hz with DisplayPort connections ( these can be converted to HDMI with separate adapters: https://plugable.com/products/dp-hdmi ). Additionally, this docking station supports four USB 3.0 ports, one USB Type-C port, gigabit Ethernet and separate 3.5mm stereo headphones and 3.5mm mono microphone jacks. The system is capable of charging over USB-C and this docking station can provide up to 60W to the host computer. This should be capable of keeping the system powered and running in all but the most extreme situations.
DisplayLink is the manufacturer of the chips and software used in our docking stations. DisplayLink software is required for the two DispayPort USB indirect graphics ports on this docking station and can be downloaded here ( https://plugable.com/drivers/displaylink ). The DisplayLink based graphics ports may not perform as well as the Alternate Mode port when the system is under heavy load or when using GPU accelerated programs and features. We recommend our docking stations with DisplayLink graphics for use with office or productivity software. Performance with graphics design, video production, stock trading, and full screen video playback may suffer from reduced performance. We do not support gaming on our DisplayLink based docking stations.
Please let me know if you have any additional questions.