How do I find resistor values for an LSTTL to ECL interface?
First, ignore R1 for now. It doesn't do anything except make sure the circuit can source current when the TTL gate is in the low state.

Now it looks like you have two equations and two unknowns:

$$-5.2 + \frac{R_3}{R_2+R_3}(V_{ol}-(-5.2)) = V_{il}$$

$$-5.2 + \frac{R_3}{R_2+R_3}(V_{oh}-(-5.2)) = V_{ih}$$

where \$V_{ol}\$ and \$V_{oh}\$ are the output voltages of the driving gate and \$V_{il}\$ and \$V_{ih}\$ are the input voltages you want to generate at the receiving gate.

But note that your unknowns (R2 and R3) appear in the same combination in both equations: \$\frac{R_3}{R_2+R_3}\$, so really there's just one unknown --- the ratio \$R_3/R_2\$. 

In order to have freedom to get whatever \$V_{ih}\$ and \$V_{il}\$ you want (within reason) you'll have to open up another degree of freedom. For example, if you could adjust the pull-down voltage (currently -5.2 V), you would be able to do this. 

One way you might do this is by putting some combination of diodes between R3 and the ECL circuit's VEE. 

Another option might be getting rid of R1 and using the fact the TTL gate can't source current in the low state to your advantage. A third resistor from the TTL output to ground could help here.