Reading between the lines, it sounds like you have a Hansen-type swing arm lamp with a 3-way switch that was intended for regular (A-lamp) socket incandescent bulbs.
Fitting the harp
These lamps typically have a shade that is attached to a "harp," a metal piece that is fastened to the socket and goes around and over the bulb.
One problem with this type of construction is that bulbs that are larger than a typical bulb may not fit inside the dimensions of the harp.
- There are CFLs that do fit and there actually is at least one 150-watt equivalent 3-way version.
- Keep in mind that you need to think in terms of lumens, not watts. A 150 watt conventional incandescent yields around 2700 lumens.
Seeking a bright, 3-way LED
While there are some LEDs that do match the A-lamp shape, they may not be as bright as you are looking for and they probably won't come in a 3-way version.
As LEDs continue to evolve, there are now some reaching the equivalent brightness of a 100 watt incandescent (1600 lumens plus or minus), but I haven't heard of anything near 150 watts equivalent in a standard shape and socket, much less a 3-way version.
There are a few 3-way LEDs now on the market, however they top out at around 75 watts (1100 lumens) on their highest setting.
An energy efficient halogen bulb
So if light output is your primary objective, then you may be stuck with incandescent (or their relatives, halogen) bulbs for the moment.
The good news is there are some that meet the energy efficient requirements. The EISA requirements, though do not apply to 3-way bulbs or to bulbs with output greater than a conventional 100 watter. In terms of energy efficient halogen 3-ways, the brightest I could find was a 100 watt maximum.
If none of those work for you, could I perhaps interest you in a new light fixture?