Certainly, Everlasting Pea (Lathyrus latifolius), native to Europe and northwestern Africa is usually propagated from seed. However, Lathyrus latifolius can also be grown from cuttings, and it is possible to root stems in water. The same is true for the annual Sweet-pea (Lathyrus odoratus), though this shoud be done very early in its growth cycle so that there is time for the cuttings to develop into flowering plants.
The OP also mentions the possibility of grafting Lathyrus. While this is not a common procedure, it is possible. Indeed, there are even described examples of successful grafts made between Sweet-pea (Lathyrus odoratus) and the Garden Pea (Pisum sativum). These grafts were made as part of the methodology of a scientific experiment involving expression of hormones in plants.
