Another male tiel ! No worries about egg laying or egg binding. 2 Males can get along just as well as a male and a female. Of course every bird is an individual, but for them to get along the best , get another tiel ! They might be able to be cage mates after 1-4 months of getting to know each other !
Almost all other species would bully the cockatiel. However, I am not positive on the matchup of lineolated parakeets, they seem more docile like cockatiels. only in the very rare cases have budgies and cockatiels got along together in the same cage. If the cage is super big, or if the two were paired together as very young and had a good friendship from the beginning , and the budgie had a laid back personality. Not all budgies have laid back personalities, a lot are spunky. I have two budgies, one is spunky, the other is laid back. The spunky one tries to knock over the other ones food dish . He also gets in his face all the time for kisses. He is super playful. Poncho is more laid back and isn't as bold.
Then you Will have the biggest chance of them being friends plus the smallest risks of injuries. What species are you thinking about?(to give more specific advise) birds like Senegals I wouldn’t let out at the same time because of the beak difference(a bit could kill your Tiel), or at least not without close supervision. Birds like lovebirds can overpower a Tiel(who are generally very easy going and Will not stand up for themselves) easily. That can lead to bullying, so again supervision is needed.
