@Ceili,
Yours is a very important question.
The original Aztec city was built from an island in the lake, and grew though chinampas (here, the wiki explanation of the chinampa method). It had several channels.
The conquistadors described it as magnificent, and similar to Venice.
If the city is over a lake, floods tend to be common.
They were so bad in the XVII Century that the city population was one fourth of what it used to be a century before.
In the late XIX Century there were still canals near downtown:
President Porfirio Díaz ordered the lake to be dried,to prevent more flooding.
During his times, ladies paid poor indians to carry them across the often flooded streets.
Since important parts of the city were built over muddy grounds, the city sinks... and water flows to the lower areas.
As for rain, my son, who lives in the UK, noticed that statistically it rains in Mexico City as much as in Cambridge. Only in England it rains every month, in Mexico City is hardly rains between late November and early March, but Tláloc certainly makes up for it in our very very showery summer.
And water takes it course, wants to go to its original bed.