The new building will be on the north side of Bridges on the Park. The residential units on the east side of Bridges on the Park will have about as much light as any building with a courtyard does. Comparable to this is AMLI Downtown which has a courtyard with four walls surrounding the pool area. The morning sun would still be just as intense since the sun rises in the east. That view would not be blocked, only the one from the north. And of course the sun sets in the west. So the most intensely sunny times of the day would be left alone.
Also the new building will have a courtyard. From the rendering it's kind of hard to tell, but it looks like the building will be U-shaped with the open side facing Bridges on the Park. That will allow more light in. This isn't going to be just a solid blocky building. The central courtyard will likely have a swimming pool, so it will be in the best interest of the developer of this building to allow as much sunlight in as possible in the courtyard. Basically this building will have a slightly smaller size footprint than Bridges on the Park, and it'll be shaped differently and slightly taller. It'll be U-shaped instead of s-shaped like Bridges is.
Here's the Google Maps aerial of the site.
http://goo.gl/maps/1V0hC
This is ridiculous. I hope the developer does a sun study to show where the sunlight and shadows will be to support their proposal, because this building is not going to block the sunlight even a little. Looking at the Google Maps images, the sun won't be blocked. If anything at certain times of the year and day, this new building may actually reflect more sunlight back at Bridges on the Park.
Also the view from the east will never go away since the land is a park. There's always going to be sunlight from that side of the property. And it's pretty useless because of the train tracks and poor access issues. And the west view is safe, too, even though the Zach Scott Theatre was built there. The thing is, Lamar is 120 feet wide. It's the same width as Congress Avenue. The south wall of this new building will be about 185 feet north of the north wall of Bridges on the Park. I measured the distance with Google Earth.