I am glad there are so many geniuses here, and very retentive geniuses at that. Yes a LP can sound like a strat. Thanks for stating the obvious with respect to differences in construction, wood, electronics. etc etc. All of that notwithstanding, with the right settings, touch and playing, yes they can sound alike. Remember, not every strat sounds the same and not every LP sounds the same. But in the universe of strats and LPs, there is overlap, which can be enhanced by settings on guitar, effects and amp. So of course a strat and LP sound different in general. But that doesn't mean you can't make one sound like the other.
Sorry for the rant on such a silly topic, but in any event, I still prefer my strat and Tele for blues. (and by the way, with my strat I can get a pretty good Santana tone - add that to the equation).