Can dongles support 240hz at 1080p?

Redditors, I got a new gaming monitor (Dell SG2522HG) which supports 240hz (FHD, rapid IPS). I play from a laptop (Lenovo Yoga 7 ProX) which does not have direct I/O port for HDMI or DisplayPort. At the moment, I can only set my monitor refersh rate at 120hz.

Hence, my question: is it possible for me to take advantage of the 240 hz with a proper dongle? [My current dongle](https://www.amazon.it/dp/B08GM2H1Q2?psc=1&ref=ppx_yo2ov_dt_b_product_details) (sry for Italian description) can support max 4k at 30hz; if I buy a similar dongle with 4k at 60hz, will it support 240hz for my monitor? ([this one for example](https://www.amazon.it/gp/product/B087QZVQJX/ref=ewc_pr_img_1?smid=A2PGPJL0BBLHLX&psc=1))

Thank you very much for your support.