How to efficiently group pairs based on shared item?

This is more like a network problem , so we using networks

import networkx as nx
G=nx.from_edgelist(L)

l=list(nx.connected_components(G))
# after that we create the map dict , for get the unique id for each nodes
mapdict={z:x for x, y in enumerate(l) for z in y }
# then append the id back to original data for groupby 
newlist=[ x+(mapdict[x[0]],)for  x in L]
import itertools
#using groupby make the same id into one sublist
newlist=sorted(newlist,key=lambda x : x[2])
yourlist=[list(y) for x , y in itertools.groupby(newlist,key=lambda x : x[2])]
yourlist
[[('A', 'B', 0), ('B', 'C', 0), ('C', 'D', 0)], [('E', 'F', 1)], [('G', 'H', 2), ('H', 'I', 2), ('G', 'I', 2), ('G', 'J', 2)]]

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To Match your output

L1,L2,L3=[[y[:2]for y in x] for x in yourlist]
L1
[('A', 'B'), ('B', 'C'), ('C', 'D')]
L2
[('E', 'F')]
L3
[('G', 'H'), ('H', 'I'), ('G', 'I'), ('G', 'J')]