Specific for Lasker during 1904 Cambridge Springs tournament I have heard that Emanuel Lasker, during the great historical tournament in 1904 (in Cambridge Springs), had to face some specific which was imposed on him. I am wondering what could be meant by that? Was there any kind of handicap with which he had to deal with? 

Most of the sources I could find on the internet do not mention any kind of special specific for Lasker.
From 1902 to 1907 Emanuel Lasker was living in the USA and concentrating more on algebra than on chess. His paper Zur Theorie der Moduln und Ideale was published in March 1905 in Mathematische Annalen and will lead to the famous Noether-Lasker theorem. 

It seems he also worked on some papers in the field of philosophy, but I know less about it.

Chess was not his main preoccupation during those years, and his participation in Cambridge Springs tournament in 1904 was a short chess parenthesis in his mathematical works.

There is no indication that Lasker was playing with any handicap in that tournament, beside lack of practice and training, and this seems very unplausible to me.

A few years later, Lasker will go back to "wasting his wonderful mind" on chess, according to a famous Einstein's quote that may be less apocryphical than most Einstein's quotes.