The Ulster front rower will join up with the squad tomorrow (Monday) and go straight onto the replacements bench for Tuesday's game against the Melbourne Rebels in place of Mako Vunipola, who has been withdrawn.
Court's Ireland colleague Paul O'Connell suffered an arm injury in the first Test win over Australia and continues to be treated and assessed.
The 32-year-old Court is coming off the back of arguably his best season to date in an Ulster jersey. He played 28 times for the province over the course of the 2012/13 campaign, scoring tries against the Dragons and Scarlets in the RaboDirect PRO12.
He made one start in the RBS 6 Nations against Scotland and lined out in Ireland's recent tour wins over America and Canada, taking his Test caps tally to 32.
Meanwhile, Lions head coach Warren Gatland has confirmed that another of the Ulster contingent Down Under, Tommy Bowe, will be in the selection mix for the second Test against the Wallabies.
Asked about Bowe's progress after recent surgery to fix a broken bone in his right hand, Gatland said: "Tommy is fit and available, he trained today and did contact."
BRITISH & IRISH LIONS Team & Replacements (v Melbourne Rebels, 2013 British & Irish Lions Tour, AAMI Park, Melbourne, Tuesday, June 25, kick-off 7.40pm local time/10.40am Irish time):
15. Rob Kearney (Leinster/Ireland)
14. Sean Maitland (Glasgow Warriors/Scotland)
13. Manu Tuilagi (Leicester Tigers/England)
12. Brad Barritt (Saracens/England)
11. Simon Zebo (Munster/Ireland)
16. Rory Best (Ulster/Ireland)
17. Tom Court (Ulster/Ireland)
18. Matt Stevens (Saracens/England)
19. Ian Evans (Ospreys/Wales)
20. Justin Tipuric (Ospreys/Wales)
21. Ben Youngs (Leicester Tigers/England)
22. Billy Twelvetrees (Gloucester/England)
23. Stuart Hogg (Glasgow Warriors/Scotland)