My Lincoln LS 2004 has the Check engine light on and the scan shows 3 problems: P0306, P0351 and P316, do you think these problems can be solved with a mayor tune up?

p0306 refers to cylinder 6 misfire detected===causes engine mechanical fault--wiring---ignition/fuel system--injector ---ECT/MAF sensor---ECM
IF there was a mechanical fault (hydraulic follower ) or valve it would be there most of the time and not just on start up. Possible injector fault but I would be inclined to check out the MAF sensor codes p0351 &2 refer to ignition coil A and ignition coil B primary /secondary--circuit malfunction === causes --wiring--ignition coil--ECM ( all causes for the both)
going on this check out the coils and check that the wiring and connections are clean and tight. basically I would be inclined to change out the coils and check /replace the MAF sensor.
change the engine --sounds like advice to get some extra money out of you.

I have a 2004 LS V8

There all bad by now

Replace all the OEM Coils that are left

My car did that once and I didn't have my gas cap on tight. Not the same model but worth trying.

it may mean you have an issue with the throtle position sensor. get free computer scan at Autozoe if check engine light is on

The light could have been triggered by literally hundreds of conditions. You need to have the vehicle computer (OBD2) scanned by a parts store (usually free), your mechanic, or a Ford/Lincoln dealer. The scan will identify the problem and you can weigh your repair options.

Misfire detected. Check spark plugs and plug wires.

What has this issue got to do with the oil change? Scan for codes and give them to me. I have a 2004 v8.

First do you have a check light on the dash? If so find the code with a scan tool. PO304 for coil four. 307 for #7 etc, if misfiring coil. You could unplug and take Ohm Meter reading, better yet an Amp Meter reading with eng running. The best would be to put a professional scan tool and oscilloscope on the ignition and other sensors and follow a series of tests to see anything is not working correctly. eg. Find some issues or problems to work on solving. You may have more than one, but you work one at a time. Don't guess and throw parts at it.

If there are 6 individual coils, sure. If it has a coil pack that plug wires run to it's not so easy.

The check engine light comes on to alert you that the computer has noted a fault in one of the car's systems. Take the car to an autoparts store and have them scan the computer for any codes it has stored. Most parts stores will do the scan for free. The codes will let you know what the computer has identified as a problem/potential problem. Hope this helped and best wishes.