Old Style Tatting is the expression I use for that early work from before the invention of the join. (Does it have any other proper name?) Motifs were joined by tying the picots together. The motifs themselves were made up of strips of tatting sewn together. Elgiva Nicholls describes the process in her book, Tatting Techniques. Butterick's Tatting and Netting of 1896 has instructions for this type of work (though not too detailed), with patterns based on studying examples of tatting that were already old at the time.
Make a strip of rings, leaving a long tail of thread at the beginning. Have a bare thread double the length of the picots between rings.
Then use that beginning tail of thread to sew the rings together. The last picot of one ring and the first picot of the next one are caught together in a little knot. Then the thread ties into the base of the next ring, sometimes fastening it to a picot of a ring of an inner round. Needle lace stitches often fill in the centers. Then many motifs are basted down onto paper to hold them in place while knots are tied to join them together.
This one little motif took me a long, long time to make. I'm sure those tatters of old, who were accustomed to this sort of work could do it much faster. Still, with the effort involved, I'm amazed tatting as an art survived until the join was invented to make it easier.