Why are there no tree-like plants that grow in lakes?
Trees need:


Deep roots to get more water and anchor their growth.
Strong trunks to support themselves against gravity.
A vascular system to move water and nutrients throughout the tree.
Small leaves that can be supported high by the trunk to compete for sunlight.


Water plants need:


Just enough root to anchor its location.
No vascular system. Water is everywhere.
Leaves that are more substantial than the stems to gather as much sunlight as possible through the cover of water.


So the kind of body that has to develop under water to thrive is in many ways the opposite of the kind of body needed to thrive on land.

Water plants would have to waste energy on 


Vast roots.
A strong trunk.
A vascular system.


...Things it wouldn't need till later while receiving little sunlight on small leaves. It would have to shed its thirsty skin like a snake on the above water parts. Too complex and little or no demand for it.



If water plants had evolved a way to turn oxygen into helium and keep much of it trapped within its leaves, then we'd have tall ocean forests. The plants could grow just like they do now  but with slightly fluffy leaves. As soon as it broke water surface, the abundance of oxygen would ramp up helium production and really fluff them leaves. The slight stems would have to be scrappy instead of massive.

There would be Greek mythology that Gaia was married to Helios but left him for Poseidon the Gaia-Shaker. Poseidon and Gaia were cursed with children (the vast ocean forests) who rebel against them and adopt a lifestyle where they are always reaching out to Helios and later in life shedd their bodies to be closer to him in spirit. Some early humans tried to rob the Helium spirits of the ocean forests by inhailing them out of their plant bodies. They were cursed and turned into chipmunks with only their hands to remind them of their past humanity.



Edit to add reference: A piece by Mickey Walburg on eHow.com

Though I would call mangroves amphibian trees, I wouldn't call them large and I was trying to ascertain the spirit of what @kai teorn was asking rather than let the question sit unanswered when I believe I can answer it. 
You learn something new often if you're looking and today @MattDMo introduced mangroves into my awareness. If he thought it was the answer to the spirit of the question post, he might have elaborated on it as an answer instead of a comment. I could be wrong about that.

Mangroves are mostly coastal. They are usually at the edges of the water. The ones that are a few meters in the water are usually more like shrubs than majestic boreal forest trees. They end up shooting roots everywhere and kinda lounge around compared to the typical tree standing straight reaching for the sun. Also the incidences of Mangroves in the ocean away from the shoreline are of maybe a handful bunched up, hardly a species wide return to the the oceans. Seen from aerial photos, Mangrove concentrations look like boreal forests surrounding lakes, not swamp lands.


  Why are there no tree-like plants that grow in lakes?
  
  Looking at aerial photos of boreal forests, with dense woods clear-cut
  by quiet lakes, I wondered why exactly are the woods so clear-cut at
  the edge of water?


I think the spirit of the next question is about trees in general in lakes. Not the few instances peppered around the world. Also some lakes grow and shrink throughout time, sometimes long enough for trees to gain a little ground and survive lake growth. But I don't think those trees as a species have developed adaptations to grow from shallow lake bottoms.


  Why won't trees develop adaptations that will let them grow from a
  shallow lake bottom, with the lower part of the trunk in the water and
  the crown above the water?


... and from the end of the post ...


  Of course there are aquatic and semi-aquatic plants like water lilies,
  Scirpus or Typha, but they are a far cry from the nearby terrestrial
  forests, in terms of biomass. Why don't they develop into large
  amphibian trees, or why don't terrestrial trees try to re-colonize
  lakes?


... I eliminated mangroves from qualification. Interesting but I still don't think it's what @kai teorn had in mind. I think @MattDMo introduced mangroves as a comment to enhance our knowledge.