Just to complicate things, the RN & RCN also built LC to their own specs.
Their version of an LCVP had steel plate on it, and had a pair of swining metal doors in the bow (famously repeatedly used as a "clip" in alomst every video of D-Day).
So, one of the reasons the USN vessel is an LCI (L), is because it's larger than the similar British LCI (and then, there's the complication that the US Army also contracted for various amphib craft--in case a person wondered why a "Mike" boat, an LCM, went from LCM-3 to LCM-5 in USN service . . .)
Like so much else, you have to have references, references, references (and references for the references <g>).