OK, if you're set on leaving and nothing will change your mind - then I guess my best guidance is "Don't lie!". Lies have an unpleasant way of catching up with a person and if you are intent on being a valued member of a challenging profession, I can almost guarantee you that you'll meet up again with former collegues in a future position. The world is a lot smaller than it seems. You don't want to have to try to remember this lie forever. If you really don't feel comfortable saying "this work isn't what I hired on for, I'm so bored I'm going back to my old position", then be vague and just say you've found a better option.
I think it's worth taking a second to ponder, though, why you are reluctant to tell the truth in this case. Leaving after a month is a pretty short span of time in a position in which you were hoping for a challenge. Not many jobs will throw you immediately into a realm of work that is so complicated you could fail at it, so often the first month is a proving ground where you're not challenged, but you're expected to learn and challenge yourself to the point where you can be more useful later on. Leaving because the company was cautious in assigning you complicated work in your first month is pretty abrupt. Have you talked to your manager about your boredom and dissatisfaction?
I'm pointing this out, because it seems like a disconnection with management is a key aspect to both of your job transitions. In the first job you mention feeling undervalued and ignored. In the second job you mention being bored, and the fact that you're leaving suggests that you don't anticipate that problem ever changing. Then you also mention symptoms of what I'd call "management disconnect" - you're leaving after a month, you don't want to tell your employer the real reason why, and the old job is hiring you back with a better offer (so I'm betting they have always valued you - whether you realized it or not). It sounds like in all these cases, there's a pattern where you aren't so clear with your management about what you really want. Managers are not mind readers - so if you haven't directly expressed dissatisfaction with either job, it's unreasonable to expect that they will know it.
My point here is that the trend of feeling underchallenged, undervalued, and ignored is going to continue in any job if you don't have a way of expressing these concerns to your management. If the old job is just a better balance for you overall, then go for it, but realize that no matter where you land, it sounds like there's got to be a better way of expressing your needs that doesn't involve changing jobs.