LISP is now the second oldest programming language in present widespread use (after FORTRAN and not counting APT, which isn't used for programming per se). It owes its longevity to two facts. First, its core occupies some kind of local optimum in the space of programming languages given that static friction discourages purely notational changes. Recursive use of conditional expressions, representation of symbolic information externally by lists and internally by list structure, and representation of program in the same way will probably have a very long life.
Second, LISP still has operational features unmatched by other language that make it a convenient vehicle for higher level systems for symbolic computation and for artificial intelligence. These include its run-time system that give good access to the features of the host machine and its operating system, its list structure internal language that makes it a good target for compiling from yet higher level languages, its compatibility with systems that produce binary or assembly level program, and the availability of its interpreter as a command language for driving other programs. (One can even conjecture that LISP owes its survival specifically to the fact that its programs are lists, which everyone, including me, has regarded as a disadvantage. Proposed replacements for LISP, e.g. POP-2 (Burstall 1968,1971), abandoned this feature in favor of an Algol-like syntax leaving no target language for higher level systems).
LISP will become obsolete when someone makes a more comprehensive language that dominates LISP practically and also gives a clear mathematical semantics to a more comprehensive set of features.