For very dense breast, what's the best imaging tool for diagnosis of a palpable lump? should i simply go straight for a biopsy?

Maybe: Imaging is very challenging in dense breasts. Alternatives to mammograms include 3d ultrasound and mri. Regardless, if you have a palpable mass i would advise a biopsy (either fine needle aspirate or core biopsy).

Mammogram and US: Whether or not your breasts are dense, the initial evaluation of a palpable breast mass should be a mammogram and ultrasound.

Need expert.: For a palpable mass, it would be most appropriate, prior to imaging, to seek an examination by a surgical oncologist with expertise in breast cancer. The expert will take a thorough history, perform a proper examination, then select the most appropriate imaging modalities for the specific findings.