Telling the length of the highest common substring between 2 words
English please!

Identifiers and comments reallly really should be in English for all code you write.  Otherwise it will be hard to impossible to take part in the completely globalized IT world we're living in.

Break long lines

Your lines shouldn't be longer than 79 characters.  Break them before binary operators:

while i + lcs_temp &lt; tamanho1 \
      and j + lcs_temp &lt; tamanho2 \
      and string1[i + lcs_temp] == string2[j + lcs_temp]:




performance related comments still under construction ;)

Ok, I got a bit hooked up here, and I think I've got something usable out of it.  I'm though not yet posting the code as it's late here and currently really a mess, so I'll tidy up tomorrow and post it then.  

Teaser (ignore the x-axis label):



Code for measurement, though killed after size 100 due to long runtime:

for size in chain(range(10, 100, 10), range(100, 1000, 100)):
    times = map(lambda v: timeit('lcsl_{}("abcdef" * {}, "cdofhij" * {})'.format(v, size, size),
                                 globals=globals(),
                                 setup='gc.collect(); gc.enable()',
                                 number=10),
                ('danieljour', 'mateus', 'aries', 'reti'))
    print(size, '\t', '\t'.join(map(str, times)))