Happy Valentine's Day, Comrades!

Here is a systematic (and therefore a bit lengthy and boring) solution. It is fun to look for shortcuts, but it is also comforting to know that there is a systematic approach.

We are given the equations

$L+R+D=24$

$3L+2R+D/2=24$

The reduced row-echelon form (rref) of this system is

$L-1.5D=-24$

$R+2.5D=48$

meaning that $L=-24+1.5D$ and $R=48-2.5D$

Now we want $L,R,D$ to be integers, which means that $D$ is an even integer.

Also, $L$ and $R$ must be non-negative, which means that $-24+1.5D\geq 0$ and $48-2.5D\geq 0$ , or, $16\leq D\leq 19.2$

With $D$ being even, that leaves us with two cases, $D=16$ and $D=18$ .

Since Nadezhda will not get any lilies when $D=16$ , Comrade Vladimir will buy $\boxed{18}$ daisies.

For consistency, we convert all the measurement to units of kopeks. So we have the following two points

1) Vladimir wants to spend a total of 2400 kopeks on exactly 24 (two dozen) flowers.

2) 1 lily costs 300 kopeks, 1 rose costs 200 kopeks, and 1 daisy costs 50 kopeks.

Let $L,R$ and $D$ denote the number of lillies, roses and daisies Vladimir bought respectively. Then from the first point, we have

$L +D + R = 24 \qquad (1)$

And from the second point, knowing that Vladimir spent a total of 2400 kopeks, we have $300L + 200R + 50D = 2400$ , or equivalently (divide both sides by 50):

$6L +D + 4R = 48 \qquad (2)$

So we have two diophantine equations. And because we know that Nadezhda loves lilies, that implies that Vladimir bought a non-zero amount of Lilies. In other words, $L > 0$ . And of course, $D,R\geq0$ .

Taking the difference of the second equation and the first equation, we have

$5L + 3R = 24 \qquad (3)$

What's left to check is to find the possible values of $L$ and $R$ . Because $5L\leq5L + 3R$ , then $5L \leq 24$ . Solving this inequality for integer $L$ gives $L =1,2,3,4$ only.

Trial and errors shows that only one value of $L$ gives an integer solution of $R$ for the equation $(3)$ , and it is $L = 3$ , with $R = 3$ . Substituting them into $(1)$ gives $D = 24 - 3 - 3 = \boxed{18}$ .