Lineolated Parakeets are considered to be peaceful. However, when keeping in colonies one square metre per couple should be available.
Socialisations with various bird species are known. Arndt (1986) reported of community aviaries with Cockatiels (Nymphicus hollandicus), Bourke's Parrots (Neophema bourkii), Plum-headed Parakeets (Psittacula cyanocephala) and Finches. Robiller (1986) could watch a budgie cock preening a young Lineolated Parakeet in a community aviary with young Lineolated Parakeets, Canary birds and Budgies.
Different breeders report on socialisation of the Lineolated Parakeets with the following bird species:

On the other side sometimes there are reports of incompatibilities (Arndt 1986; however, there are no concrete examples)

Low (1983) as well as de Grahl (1985) dissuade from socialisation of the Lineolated Parakeets with larger parrots or other larger birds, as Lineolated Parakeets do not defend themselves against attacks of those, reputedly. So, it could lead to extreme injuries or even death of the birds.
In my opinion it isn't understandable, that they are called "born victims" as it is often done. Normally, when tussling with budgies always the budgies lose. Keeping Lineolated Parakeets together with cockatiels, in case of doubts, will be only problematic for the cockatiels. Additionally Grigull (1976) writes: "This year I kept them together with 1.1 Cockatiels in a larger aviary, but I had to catch them out of it in April, as the Cockatiels hardly could reach the food."
These statements refer to healthy and strong animals. Enough space must be provided, so that they can keep out of the their way. Moreover, it has to be mentioned, that there are individual differences among the Lineolated Parakeets as well. You can meet especially vivacious, reckless specimen as well as shy and reserved ones.
That's why naturally it is important to accurately observe the animals during socialisation, for being able to interrupt severe conflicts and separate them if necessary.