Hmmmm not a lie to say it's possible EU membership could be retained or applied for in a quick rejoining. It was all very much a special circumstance, who knows how it would have played out, it still seems unlikely Scotland would have been left out in the cold for very long, being a country wanting to be part of the EU, already complying with EU laws in totality, and with strong resources that the EU would welcome back in. Huge renewables potential for the future, a key asset in decades to come. There were overtures coming from various EU countries to state we would be looked on favourably. Would it have been instant, probably not, no, but to say it's a lie we couldn't have ultimately been in the EU as an independent nation is absolutely incorrect.
Meanwhile the Brexit referendum was sold on an absolute pack of lies and over simplification and seemingly a have your cake and eat it approach from the Brexiters, a referendum that's now sold Scotland down the river completely, shafting the majority here who wanted to remain.
The SNP claim of retaining EU Membership was absolutely a lie though, and is completely comparable to some of the lies told in the Brexit referendum, it wasn't even the only one either.
The SNP continually claimed that they could retain EU membership, despite EU rules saying otherwise. Hell, even when the EU themselves intervened and clarified that they wouldn't they persisted with the claim.
Similarly were the currency union claims. Despite Westminster continually saying that there would absolutely not be a formal currency union in the event of Scottish Indepdendence, the SNP continued to insist that there would be. It stank of the have your cake and eat it claims that were later seen in the EU referendum.
"We will retain EU membership, we will have a formal currency union, we will only take this much of the national debt" etc etc. To say nothing of the economic plans, or almost complete lack thereof (The oil will pay for it).
Nobody was saying that Scotland wouldn't be able to re-join the EU eventually, but the SNP claims were not of re-joining, but of retaining the existing membership and that there would never be a period where Scotland was outside of the EU. That was a lie and they knew it at the time of saying it.