After heavy weight lifting workout, if I don't eat any proteins, will my body use my fats to recover the muscles and make me more lean?
To answer your question directly, yes, if you regularly perform heavy weight lifting workouts and restrict your calories generally (i.e., the timing isn't all that important), you will lose weight, and possibly get a sexy, lean look, but that will depend entirely on how much muscle you already have. If you're strong and fat, and you lift weights, and don't eat much? You'll end up strong and skinny. Good! You'll likely even get "stronger" as time goes on, as your muscles become more efficient. Weight lifting is the best thing you can do to lose weight and maintain muscle mass. In fact, the research shows that dieting in the absence of weight lifting will result in roughly a 75%/25% ratio of fat to muscle loss; for every pound you lose, a quarter of that pound is muscle, but not if you regularly lift heavy weights!
To build new muscle, however, you need Essential Amino Acids, which are found in protein sources, e.g., meat, eggs, and dairy. Protein is also found in nuts/seeds/vegetables/grains, but that protein is less "complete" and less "bio-available" than the protein found in meat, eggs and dairy. The protein-to-calorie ratio in nuts/seeds/grains (yes, even quinoa, despite it being a "complete" protein source) also makes them a poor candidate for a protein source if you're trying to lean out. One of the worst pieces of nutrition advice I see floating around is to tell somebody who's trying to lose weight to eat either nuts or nut butters. Don't do it.
Consuming sufficient protein also protects against muscle loss while being "hypo-caloric," which is just a term for eating less than calories than you expend.
In addition to eating protein, you can also consume essential amino acids in an extremely low-calorie supplement form. Look into "Master Amino Pattern" a/k/a "MAP" and the research conducted thereon. (There are a number of sellers of the exact same product, and they cost pretty much the exact same price.) MAP is 99% bio-available protein. For comparison, protein in steak is about 30% bio-available. What this means is that 10 grams of MAP, which is, by the way, only 4 calories total, is equal to 30 grams of protein from steak, which is equal to at least 120 calories, and usually significantly more, because steak is almost never fat-free, and if it was, it would be gross. MAP is expensive-ish and can typically be purchased for around $2/10 grams on Amazon - what many consider a "serving," notwithstanding the bottle telling you that five grams is a serving.
If you want to gain muscle while staying hypo-caloric, then you need to eat sufficient protein or supplement with sufficient essential amino acids, the general recommendation for protein is 1 gram per pound of lean mass. Note, you can gain muscle and lose fat at the same time, but the amount of muscle you gain will be small, and even less if you're already fairly muscular.
If you wanted to get most of your protein from MAP, you can (the science supports this, think 20 grams a day of map plus a couple of chicken breasts), but I wouldn't recommend it, because food is delicious and cutting calories by cutting protein is the least efficient way to reduce total caloric intake. Your body expends significantly more energy in the digestion and utilization of protein than it does digesting either fat or carbs. You would be better off reducing fat intake, or, even better, carbohydrates, if your goal is weight loss, while increasing the amount of protein you consume.
Don't skimp on protein when trying to lose weight, and, if you do, supplement with MAP.
Also, if you're lifting weights, supplement with creatine. This advice applies to everybody lifting weights. Creatine is cheap, it works, and has little-to-no side effects.
If you're trying to gain as much muscle as fast as possible, you need to be hypercaloric (consuming more calories than you expend) and you should eat protein and carbs directly after lifting. If you do this, you will also gain, not lose, fat.
Despite the info-dump above, there's a lot more out there!
Last piece of advice, do not go too hypocaloric too quickly! Rapid reduction in daily caloric intake will dramatically reduce the hormone leptin and make it very, very difficult to lose weight.
Hope this is useful!