Although it may seem like... well, no, this is possibly more than false, due to one fact. Social media consultancies generally wouldn't be aware of these types of things unless they were announced weeks in advance. And if the decision was for it to come out in September, well... wouldn't it be logical that by now we'd have a trailer or something? Something that shows us what the console is really like?
So, I don't really see this as evidence that it will come out in September... what they might consider possible is the timeframes in which handhelds were sold this year.
For example, the Legion Go S Windows OS and Legion Go S Steam OS took a total of 2 to 4 months. So, from May to September, that's 4 months. So... it makes sense that they'd sell it in September at that point.