I like Imogen and Romy best of your girls' names. Libby and Dotty are sweet but IMO they need a longer formal name. How about Kitty, Callie, Ivy, Nola/Nova, Wren?
I love Rory, Leo, Teddy, Dexter and Levi from your boys. Don't like Camden and Heath and I can see where you're coming from on Ziggy and Titus but I think they're too out there and too teaseworthy to actually use.
Lola - Love this - probably my favourite on your list, although not overly popular on here
Aubrey - Not a fan. This is traditionally masculine, but I do think it sounds more feminine than masculine. I prefer Audrey.
Hallie - Not a fan.
Romy - Not a fan. I don't know why I don't like this, because I love Remy for a boy.
Dotty - Sweet as a nickname, but doesn't work as a standalone name.
Libby - Again, sweet as a nickname for Elizabeth but not as a full name.
Titus - Please don't. It's one letter away from tits, and even if that were a non-issue, it's hugely aspirational and very out of place among your other names
Rory - Love this
Leo - Love this
Heath - This is nice and very underused
Teddy - Dislike. Very popular and very insubstational as a standalone name. It's fine as a nickname for Theodore or Edward though.
Camden - I like this, but it might be odd if you're from the London/greater London/whole of England possibly areas, as the place is very well known. This wouldn't be an association in Australia, the US, Canada etc. so would work well as a name there.
Dexter - I like this but not the association with the TV show (and character!)
Levi - This is seen as a bit "tacky" where I live.