Yes, it is possible to build chips without lithography. In the traditional chip manufacturing process, lithography machines are used to project circuit patterns onto silicon wafers. However, with the development of technology, some new manufacturing methods have emerged, such as self-assembly technology and nano-printing technology, which can manufacture chips without the use of lithography machines.
These new technologies can make chips more efficiently and cheaply, while also helping to solve some of the limitations and challenges of the photolithographic machine building process. Therefore, making chips without lithography mechanism is a real existence.