Solution

s=10;
r=28;
b=8/3;
eqn1=x'[t]==s* (y[t]-x[t]);
eqn2=y'[t]==r*x[t]-x[t]*z[t]-y[t];
eqn3=z'[t]==x[t] y[t]-b*z[t];
eqn4=x[0]==0;
eqn5=y[0]==1;
eqn6=z[0]==0;

soln=NDSolve[{eqn1,eqn2,eqn3,eqn4,eqn5,eqn6},{x,y,z},{t,0,60}]

ParametricPlot3D[Evaluate[{x[t],y[t],z[t]}/.soln],{t,0,60},PlotRange->All, AxesLabel->{x,y,z},PlotStyle->Red]