I'm not sure how much consensus there is, but the latest discussion that I'm aware of (Drost, 2014) rehabilitates the Lyonese style "continental mint invasion coinage" as simply the first issue minted at Lyons itself. He presents a variety of evidence for this, including a die link from one of these unmarked marked coins to the Lyonese PLA issue.
There is also the unmarked London "intermediate group" immediately following the first "LON" coins, which RIC omits. I believe these were first written about by Mossop in 1958, then Basten in 1959 and later in NC 1971 where he illustrates the stylistic continuity from the LON coins through the intermediate group into the later class II group. There is also Stewartby's later NC 1998 paper discussing these.
So, from London in date order we have:
1) LON = Stewartby 1a = CT 1.01 laureate
2) Stewartby intermediate Ib = CT 1.02 laureate
3) Stewartby intermediate IIe = CT 1.03 LC (+ rarely LDC), cuirasse typically with >>> chevron decoratoin
3) RIC Class IIa, IIb = CT 2.x
4) RIC Class III = CT 3.xBastien - Some Comments on the Coinage of the London Mint, AD 297-313 (NC 1971)
Stewartby - Early Tetrarchic Coins of London from the Market Stainton Finds (NC 1998)
Drost - Les nummi sans marque de style lyonnais (Rev Num 2014)
Here's some examples:
Lyons first unmarked issue
London Ia
London intermediate Ib
London intermediate IIe
London IIa