I think your "__?__" entry should read "binary-to-bcd converter >>> "bcd-to-seven-segment decoder-drivers".
You could program an EPROM to function as the binary-to-bcd converter and use 4543 (or 14543) driver chips, since they're designed to drive lcd's.
That's if you have to use the ADC0804. Is it required that you use it? Since the ICL7107 has an ADC in it, you could just connect the output of the LM35 directly to the input of the ICL7107, like Brevor said. Scaled appropriately, you could theoretically get a 0-200C display. That's assuming 10mV/deg C output from the LM35 and a full scale of 2V. The LM35 will only sense -55C to +150C, but it will still make very useful thermometer. Also, to drive an LCD, you'll need the ICL7106.
Jeff