Two linked questions about domestic to international transit:

1) There's a lot of info in this thread about domestic to intl on the same airline, and intl to intl. I am connecting from AI (domestic) to LH (to Munich and onward) with a 5.5 hour layover. Are the transfer counters able to process LH tickets, especially so far in advance of the connecting flight?

2) Once in the international wing of T3, it looks like there are 3 Star Alliance lounges open at that time, and I am *G. In my past experience, lounges in India have required invitations. Is it possible to visit multiple lounges on the same departure? Is it necessary, then, to get multiple invitations?

Thanks.