Generate lazy values
JavaScript (ES6), 31 bytes

n=&gt;~-(n*9+4).toPrecision(1)/9|0


Directly computes the lazy value for each n.

Edit: Only works up to 277777778 due to the limitations of JavaScript's integer type. Alternative versions:

n=&gt;((n*9+4).toPrecision(1)-1)/9&gt;&gt;&gt;0


35 bytes, works up to 16666666667.

n=&gt;((n=(n*9+4).toPrecision(1))-n[0])/9


38 bytes, works up to 944444444444443. But that's still some way short of 253 which is 9007199254740992.