Well - I didn't get any replies but I did figure it out. Just in case someone else needs this information, here goes:
The bad relay is part number 90987-02022 and the label inside the fuse box lid is "MG CLT" which stands for "magnetic clutch". It has to be replaced with part number 90987-02028 (according to LEXUS Technical bulletin EL009-05) which will cost between $70 and $100 depending on which dealer you go to (Toyota carries this too). I bought one, plugged it in and voila, the blinking stopped and the air conditioning started working again.
Hope this helps someone.