Can we see lava in a divergent tectonic boundary?
No, we can't. This is because of several reasons, mostly stemming from the fact that the plates are not diverging fast enough to keep the lava hot enough before it cools down.

If we go and look on diverging plate boundaries on land, such as on Iceland or East Africa, you don't have a "line" of lava. Instead, you have individual volcanoes located along a linear trend:



source: http://volcano.oregonstate.edu/vwdocs/volc_images/africa/africa.html

You see all the volcanoes along a line in the Ethiopia and Kenya region? It's not one "line of lava", but single volcanoes along a line.

If we think about divergent boundaries underwater, where the lava comes from a much shallower depth, we may think it might be possible to see this kind of feature. The problem is that water is extremely effective in cooling down lava. Here's an example video of what happens when there is lava underwater:

https://www.youtube.com/watch?v=hmMlspNoZMs

As you can see, the lava cools in seconds. It doesn't erupt fast enough to sustain a constant liquid lava "line" under water.

This is not something that happens on Earth. But on other planets, maybe. If we think of a planet where the surface temperatures are on the hundreds of degrees Celsius (such as Venus), the cooling of the lava may be slow enough for plate tectonics (if they exist on said planet) to catch up and provide enough magma to sustain a long-lived magma lake-river on the boundary.