Index Match both ID and next highest date between two spreadsheets

I could use some help, I use VLOOKUP all the time to take two reports from our system to find matches. But, this problem is a little different. I have the following spreadsheets:

Spreadsheet 1: each client ID will have one one row associated with it - this is their date of discharge from another facility. Columns in bold.

CLIENT ID


DISCHARGE DATE

Spreadsheet 2 - This spreadsheet could have thousands of rows with multiple dates of services occuring
CLIENT ID (will match spreadsheet 1)


DATE OF SERVICE

These are the only columns that really matter. I want to find the first service the client had after their date of discharge from the other facility. I don't care about the dates prior. And I don't care about subsequent dates. They could show up many times but I want the one just after the discharge date. I am fine with N/As, this is quick and dirty to feed something else. I couldn't figure out to make VLOOKUP work for this.

Can anyone help? I tried INDEX MATCH and it was a failure. We're so busy as a healthcare facility I can't afford to put much more time to this. Any help would be appreciated!