Hello. Are dispensation, or when the diocese grants a free to marry due to lack of form, acceptable from a traditional perspective? Is the person free to marry? 

You'd have to ask them. They don't accept what comes from the "diocese" for obvious reasons, but they do recognize that lack of form can make a marriage invalid. Best thing to do is go in and tell them the details.

It will also probably depend on what "traditional" means here.  It could be FSSP or ICKSP.

Lack of form is probably one of the most straightforward and could easily be verified.  Of course, the NO has applied "lack of form" to Catholics whose marriages were witnessed by a Traditional priest.

Aren’t they kinda being internally consistent there though?

Usually, nothing that comes form the diocese is trustworthy. 

I wouldn't risk my soul based on something that diocesan authorities decided.

I would advise you to study the Church laws very deeply on your own. You should also seek the opinion of many good Traditionalist priests.

If there are children involved, you are married. 

Annulments were never meant for those with children.

What in the world are you talking about?  I've rarely seen such nonsense.  What's even more shocking is that someone upthumbed this post.

One could argue that if you have children, you SHOULD remain together and get the marriage sanated or fixed ... if possible.  In some cases it's not possible and the Church MAY under some very strict circuмstances permit you to remain together as brother and sister for the sake of the children.

But, no, it's absolutely not true that "if there are children involved, you are married."  There are a thousand scenarios where this is not true.  Let's say that a woman divorces her legitimate husband, then shacks up with some other guy and has children with him.  They are most certainly not married and cannot be married until her first husband dies and then they marry legitimately.  Until such a time, they are most certainly not married, despite the children.

And what is this "Annulments were never meant ..."?  You seem to have this notion that annulments are proceedings of some kind that sever the bond between a married couple.  They're nothing more than findings of fact.

If you don't know what you're talking about, please refrain from posting.

If there are children involved, you are married. 
Annulments were never meant for those with children.

Illegitimate children are born all the time. Children can come as the result of fornication, adultery, etc. The presence of children in no way proves their parents are validly married.