In this paper, the relation between the modified Lorenz boosts, proposed in the doubly relativity theories and a linear combination of Conformal Group generators in R-1,R-d-1 is investigated. The introduction of a new generator is proposed in order to deform the Conformal Group to achieve the connection conjectured. The new generator is obtained through a formal dimensional reduction from a free massless particle living in a R-2,R-d space. Due to this treatment it is possible to say that even DSR theories modify lightcone structure in R-1,R-d-1, it could remains, in some cases, untouched in R-2,R-d.
