I need to use a program that only runs under the classic OS and would like to know what a good one is or if this is a way to run it in Mac OS Lion. Any suggestions will be appreciated.

Yes, Sheepshaver. Macintosh Emulator.

Or if it works under 68k, Basilisk II or MiniVMac.

I have used Macintosh Emulator for some time and it work in a stable way. Try it.

A good resource for emulators, along with guides, is http://www.emaculation.com

Can you tell me what type of Classic application it is? When was it released? Was it designed for PowerPC or 68k?
If it was designed for PowerPC, it MAY work in Classic on versions of Mac OS X prior to 10.4. But from your original post, I take it that you don't have that.
Mac OS X Lion sadly doesn't support Classic applications anymore, so you have to emulate them.

Depending on the release date of your application or the platform, only one specific emulator will work.

If it was released for very early Macintoshes (such as the 128-512k, SE, Plus, Classic, etc), you need Mini vMac, which can be found at the following link : http://minivmac.sourceforge.net
Mini vMac requires a ROM file for a Macintosh Plus, which can be found in various places or can be dumped from an actual Macintosh.

If it was released for later Macintoshes such as the Macintosh II series, early-to-mid LC series, Performa or Quadras using a 680x0 processor, you should try BasiliskII. This emulates various 680x0 Macintoshes, but it's very outdated and I haven't had much luck getting it to run on a modern machine... http://basilisk.cebix.net/

Most PowerPC (and later 68000 ones) can run on SheepShaver, a emulator which emulates a early PowerPC Macintosh. It works nicely. http://www.emaculation.com/doku.php/sheepshaver

If all else fails, you could try PearPC.

Mini vMac emulates System 0.85 - System 7.5.3, while BasiliskII emulates System 4.0 - System 8.5, and SheepShaver emulates 7.6.1 - 9.2.1...

All emulators require ROM files, and you can find them in various locations around the internet or they can be dumped from a real Macintosh.

SheepShaver maxes out at 9.0.4.

Absolutely, and if you want to easilly get Mac OS 9.0 in nearly any language, you should use "Mac OS Anthology '99" DVDs ...

Doesn't BasiliskII max out at 8.1? AFAIK it is the last 68k compatible version of the Mac OS.

It does, there's no emulator currently that runs 8.5.

I thought Sheepshaver ran all the PPC OSes up to 9.0.4?

Yeah you're right, it does support 8.5.

Sheepshaver does not emulate NuBus Power Mac-specified System, including all versions of 7.1.2, 7.5.0 and 7.5.1.

And any application that requires MMU, low-level hardware access, low-level disk access and/or precise timing will not work in Sheepshaver.

Actually OS 9 capable machines are cheap on eBay and similar sites, you could get one to work on a real Classic OS environment.

Indeed, I remember buying my iMac G3 DV SE 500 MHz (Snow) for 100 zlotys, which is about 30 bucks. Mac OS 9 runs flawlessly, it can even run Unreal and Quake III Arena at acceptable speeds. If you really need a stable solution to run your Mac OS 9 app, buying an old mac is the way to go.