Yes, though I'm not that familiar with the Duggars, I think it could have been a micro version of that with Lilly the oldest living with Jack just 2 years younger, and Meadow, at 1 1/2 years old, perhaps being the focus of her bioligical parent's parenting energies with the older 2 attending public school and being closer in age.
And having come from the same biological parents and for a few years being raised by MBM & CS, and then together as young siblings they began living with DM as their mother's newer partner 3 years before, so when they were 3ish (Lilly) and 1ish (Jack), and then along came Meadow from a newborn to a 1 1/2 year old, their stepdad's daughter by their mother.
IMO, these circumstances of their upbringing, for little Lilly and littler Jack in the last 3 years living with DM and his family on their property with their mother and his daughterbcould have tightened the bonds between them, and Lilly could have felt she needed or wanted to take care of him and been more in charge of looking after Jack than may be typical in a family unit with 3 kids all of them their own.
It may not be the case here, but if it was, Lilly could have felt some pressure to keep Jack in line and/or off their custodial parent's radar, and/or out of harm's way as best she could, which could have led to her taking drastic measures, e.g., saying to Jack "Mom called us in sick, our parents are tired & sleeping in with Meadow, the weather is getting better, and we don't want to bother them, so let's go...
[Insert scenario under which they could have left home under their own volition] to keep away from any negative situation that may arise for now..."
I know this scenario is maybe somewhat adultified and unlikely and unproven, but it is a possibility, IMO, that things at home were not great for them, and perhaps they were planning to run away or meet up with someone, under which they disappeared because they could only take it so far/it was a fantasy which grew legs that they lacked the maturity and/or understanding of what it would look like in reality to escape their circumstances, and/or someone intervened on their plans and stopped them from going through with their plans for that day with parents having a lay in according to them, and they only had a cough that didn't stop them from taking advantage of some free time doing what they wanted.
JMO
although I have kids the same age now and no way in heck would I let them be home alone (yet - more because my oldest gets distracted easy and newly on a smart phone so not as attentive) but I try to raise them a bit '80s style' and make them independent like I was as a kid that age with other "responsibilities" hahaha...
