In terms of etymology, みずうみ is indeed derived from two words, but it's now a single word—much like how English housewife is a single word, even though it's clearly derived from house + wife.
This doesn't really matter for how you pronounce two /u/ vowels in a row, though. You just hold the sound for an extra beat ("mora"), like it's a long vowel:
ː symbol indicates a long vowel and the
ꜜ symbol indicates a noticeable drop in pitch.
The drop in pitch is called a "pitch accent", and in this word it occurs after the second /u/ sound. The red line in the following shows the basic pitch pattern of the word, rising after the first /mi/ and falling after the second /u/:
I've checked four dictionaries, and all four say the pitch accent is in this location. However, several users have commented saying that the accent is often moved one mora to the left:
In any case, you can listen to a recording of this word that someone uploaded on Forvo.