matching with a look function with conditions

Hello,

I'm new on this forum, and thanks in advance for all the help that you will give me.

I need to compile in the file attached the column in red "OLD ID" with one of the value searched in the column "OLD ID" on the right when the type is the same and with the conditions that The date on the right "inv. date" has to be before of the "Del. date" on the left. the ID can appear only one time.
is it possible to resolve this problem with a look.up function or an index/match function or i need to use a macro VBA? i know that both of the solution if finds multiple result, give the first value that fits the conditions, but it's possible to skip the first if it's already used in a previous line or if the other conditions don't fits?

Can you help me?
THANKS!!!!