Can all on 4 implants be done without a sinus lift?

All on four was developed as a "graftless method" to reconstruct an arch with dental implants. In years past, it was taught that the upper arch needed 8-10 implants and the lower arch needed 6-8 implants when reconstructing with dental implants and that the implants needed to be perpendicular to the bite forces (no tilting). This usually required bone grafting, including sinus lifts, in order to have enough bone to place so many implants in the "correct" locations.

Tilting implants and only having 4 was originally viewed as below standard of care, but is now viewed as normal or common.

You can place a full set or upper set of implant-supported teeth without sinus lifts or bone grafting using zygomatic implants. Thanks to modern research leading to the advancement of zygomatic dental implants, patients who have been told they are not candidates for conventional dental implants, can be treated successfully. Designed specifically for patients with bone loss, zygomatic implants are tilted and much longer than traditional dental implants. While traditional implants are placed in the jawbone, zygomatic dental implants are placed in the cheekbone which is very dense and provides excellent support. 

Traditionally, All-On-4 dental implant procedures allow patients to avoid sinus lift surgery.  With this style of treatment, the implants farthest back in the mouth are typically angled forward up to 45 degrees.  Placing the back implants in this manner avoids the sinus and allows longer implants to be placed that provide an increased amount of bone-to-implant contact.  
With that being said, in certain situations, sinus lifts may be required for All-On-4 style dental implant surgery.  In some patients, the sinuses have enlarged so much, that there is not enough bone remaining to allow for All-On-4 procedures.  In such circumstances, sinus lifts may be required to allow for dental implant placement.  An alternative to sinus lifts in these situations is sometimes a zygomatic dental implant, but these implants have their own inherent issues.  
In performing over 1,000 All-On-4 style dental implant procedures, I have only "had" to do sinus lifts in less than 4% of cases.  Essentially, most All-On-4 style cases can be done without sinus lift surgery.