I am trying to purify an hydrophobic recombinant protein containing a His-Tag. Is there any suggestion about lysis and wash buffers? To eluate I am using imidazole.
You can use RIPA, M-PER, or B-PER buffer in tris or phosphate buffer to extract membrane proteins (assuming membrane protein since you said hydrophobic). You may also add some urea to improve solubilization. Use french press, bead beat, or ultrasound-assisted physical disruption methods to lysis. After pelleting the other cell components, collect the supernatant and follow the Co-NTA or Ni-NTA purification by performing an imidazole gradient. Apply SEC as the second polishing step which is typical for tandem purification procedure when IMAC has been chosen.
while very hydrophobic proteins (like membrane spanning regions on membrane proteins mentioned by Ismail) can require full solubilization by detergents, there are cases where lower levels of hydrophobicity can be addressed with simply including an "organic modifier" in the typical IMAC purification. These can include solvents (AcCN or methanol, to 10-20% v/v after testing for precipitation!) or even NDSB's or higher CMC detergents below their CMC values. Good luck!
As others mentioned above, membrane proteins are a little bit more tricks, if that is what you are referring to by "hydrophobic proteins".
However, I would recommend something besides detergents. It is a bit dated method. I would recommend nanodiscs here. Especially the ones based on synthetic polymers (DIBMA, SMA, AASTY).