Neither of these is a website
This is a counter-to-counter pair, and that changes what the connection is for.
Square and Lightspeed are both point-of-sale systems, so this pair is usually two counters rather than a counter and a website. A second location, a concession running a different till, a shop that kept Lightspeed while a newer site went to Square: all of them end up with two registers selling from stock that is really one pile. Neither system reads the other’s catalogue, and left alone the two counts separate within a weekend.
Both sides push their changes to us immediately, so neither register is waiting on a timer. That is the right behaviour for tills, where two people can ring up the last of something within the same minute and neither can see the other’s screen. QuickSync keeps a single figure that both registers are corrected against, so neither till has to be nominated as the master.
The one number to check before you connect is SKU length. Square stores 80 characters and Lightspeed takes 64, so 64 governs. Anything longer arrives at Lightspeed truncated and stops matching the item it came from, without an error to tell you. Sixty-four is generous enough that most catalogues never notice, which makes this a five-minute sort by SKU length rather than a piece of work.