I've found if you go back a page (press back arrow top left) and start again it will usually sync up. You can unplug it to reboot it and it seems to work for awhile also. This is an annoying issue that I wish Roku would fix.
I have the identical problem with a 4640X 4k ULTIMATE hooked to a 4K Spectre TV. OTA TV fine, DVD playback fine. Have 2 other 1080P TVs using a Roku 3 -no audio lag problems. Will try some of the suggestions but nothing has worked up to now. Definitely a Roku 4 only problem. Ordered a super HDMI cable to try also.