Preface -- tradition isn't science. And it isn't exactly tradition either.
Historically, most lagers -- the ones called "Lager" or "Winter beer" -- were fermented fairly rapidly at moderate temperatures and then held cold for only a week to ten days to clarify. This was adapted, during the period when brewing from April to September was prohibited in Bavaria, to the process for "Summer" or "March" beer, where temperature was dropped before fermentation was complete, to slow the conditioning process and combine it with the cold clarification period. This was done to ensure a supply of ripening beer through the warm months, before refrigeration and legal reforms rendered it unnecessary. But it does not in fact provide the optimal conditions for either conditioning (flavor development by yeast) or physical stabilization (clarification and, to a lesser extent, rounding of flavor by precipitation of certain substances.)
Flavor maturation is best achieved at warm temperatures, up to room temperature, where yeast is most active. Below 40°F, yeast won't do anything, so conditioning will not really continue. If you include a "diacetyl rest," raising the temperature of the beer well before terminal gravity is reached to invigorate the yeast, the flavor will be as developed as it is going to get by the time fermentation finishes. With many yeasts, even this is unnecessary. Once flavor maturation is achieved -- fermentation byproducts reduced and sulfur scrubbed out by CO2 -- all that really remains is to drop the yeast and form and precipitate chill haze, physical (not fermentation) processes that are best accomplished at cold temperatures. This may take a long time, or not. You can accelerate it by fining or filtering. But when the beer is clear, there's no real benefit to extending cold storage.
So to your question, yes, the beer can be conditioned warm and given a brief cold rest to clarify. But there's no benefit to extending either rest beyond what's needed to achieve the goal. A few days warm and cold crash can work. In any case, whenever the beer seems ready to move on, it is. Let it guide you. That's often thought of as a very modern, accelerated process. But it's also very traditional.