The answer is 2.

**
This section requires Javascript.
**

You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.

The points of intersection of coordinate axes with given lines are $A(-3,0),B(0,\frac{3}{2}),C(0,1),D(\frac{-1}{\lambda},0)$

These $4$ points must be concyclic.

$\text{Case 1:}$ Two of the points are same as $3$ points are always concyclic.

$\text{Case 1.1:}$ $A=D\Rightarrow \frac{-1}{\lambda}=-3\Rightarrow \lambda=\frac{1}{3}$

$\text{Case 1.2:}$ No $D$ exists. That is, first line is parallel to x-axis. $\lambda=0$

$\text{Case 2:}$ $OA\times OD=OB\times OC\Rightarrow \lambda=2$

$PS:$ You may use any other condition as well in Case 2.

$\lceil 0\times 2\times \frac{1}{3}\rceil+\lfloor 0+2+\frac{1}{3}\rfloor=1+2=\boxed{2}$