Over the decades there has been a lot of papers devoted to the classification of Lie algebras of low dimension. Do you know any paper dealing with the problem of determining (up to restricted isomorphisms) restricted Lie algebras $(L,[p])$ of low dimension over a field of characteristic $p>0$?
As far as I know this type of classification problem has attracted very limited attention over the years. That's probably due in part to lack of enough external motivation, coupled with the cautionary example of rapid growth in numbers of nonisomorphic Lie algebras in characteristic 0 as the dimension increases (nilpotent Lie algebras for instance). There are some algorithmic possibilities in prime characteristic nowadays. A treatise by Willem de Graaf covers a lot of ground but may not help directly with your specific question: Lie algebras: theory and algorithms. NorthHolland Mathematical Library, 56. NorthHolland Publishing Co., Amsterdam, 2000. The main output of papers on classification in recent decades has involved simple Lie algebras (restricted or not) in prime characteristic, with the most definitive solution found for $p>3$ by Premet and Strade in a series of papers (and monographs). 


H. Strade, Lie algebras of small dimension, Contemp. Math. 442 (2007), 232265; arXiv:math/0601413  classifies nonsolvable Lie algebras of dimension <7 over a finite field. I think there is a corresponding GAP package. Another seemingly relevant reference: M. VaughanLee, Simple Lie algebras of low dimension over GF(2), LMS J. Comput. Math. 9 (2006), 174192. 

