Yes, you can update the raspberry pi firmware through Lakka over SSH, I’ve done it twice so far.
There’s a good guide here on the raspberry pi forum:
The post is from a Pi engineer, which is good, but it’s disappointing that this lives just in their forum and not on a proper page. Personally, I downloaded the posted file to my PC, copied it to my Pi over SAMBA, and then executed the logic described in his post. Note that the file has been updated since his post, so the filename posted at their Google Drive (!?) has changed, so you will have to slightly modify the script.
It is definitely a good idea to patch your Pi4 firmware - the USB stack on the stock firmware has real problems, and there are heat (which means power waste) problems too.