This is an unnatural English sentence. What does it mean? He loved her then, but he doesn't love her now?
I think the English sentence is OK. It's the situation the sentence is describing that is unusual.
I think it depends on the context, and it need not be negative. Imagine this conversation:
Q: You two seem to be getting close. Do you love her now?
A: I loved her a week ago. And now I love her even more.
Yes, there can be an unspoken "already"/"už" hidden in both the English and the Czech statement. :) So it doesn't necessarily have to mean "He loved her then, but doesn't love her anymore."
Is this the same as saying "A week ago he was in love with her"
No, although the meaning is quite close. "To be in love with" is "být zamilovaný do + Gen".