We don't know as much about Spartan shields as we'd like. I've written about the various possibilities as to their colour here, which also includes a bit about the lambdas.

The main point is that only one source, a fragment from a lost comedy by Eupolis, actually proves this practice, by using the metaphor "gleaming lambdas" to refer to an approaching Spartan army. The fragment probably dates to 422/1 BC. Before this time, nothing suggests that the Spartans used a uniform shield emblem. It is possible that they adopted it around the time of the Peloponnesian War. However, since this fragment makes no sense if there were no lambdas visible on an approaching Spartan, it seems very likely that they did indeed carry lambdas on their shields.

Other evidence for uniform emblems shows that standardised shield blazons were a feature of Classical Greek warfare. We know that the Sikyonians had a sigma on their shields, and the Mantineians a trident (in honour of Poseidon); by the 4th century BC, the Thebans emblazoned their shields with a club of Herakles. When the Messenians were liberated in 370 BC, they started using shields with the letter M on them. While none of this confirms the use of the lambda by the Spartans, it suggests a common practice that the Spartans may well have shared, perhaps even initiated. Since the Spartans cared a lot about looking the same so as to intimidate their enemies, they wouldn't have missed this opportunity to create an iconic feature for others to fear.

I don't know what Angus McBride has said on this, do you have a link or a quote?