Why is my 2004 Lincoln LS shaking when I reach 70 mph

check your wheels balance,If the problem still check your rims whether you have any slight bend,

have your suspenion checked you may have a bad tire

If the shake changed by changing tires,you may be close to the fix.Sure sounds like a wheel or tire or rotor is out of balance.I would have all of the wheel/tires balanced on a NAME BRAND freshly calibrated dynamic motorized wheel balancer.

It's either:

1. Out of alignment or
2. Front tires are not properly balanced.

Either way you should have it repaired by a mechanic soon. Your destroying your tires and can cause front end damage.
HINT: Have the tires Dynamic balanced, not Static balanced. It cost a few dollars extra, but saves you twice as much in reduced tire wear.

This is often the result of a tire that is out of balance. Check for bubbles on any of the tires and have the tires balanced. That should clear up the problem.

It could be as simple as your tire balance is off.

Tires need to be balanced. Take it to a tire shop and ask them to balance all 4 wheels. Problem will be fixed.

Tires would be the 1st place to check. If you seem to feel it more in your legs then it is likely the front, if felt more in seat bottom then could be a rear tire. Depending on how severe the vibration is there could be a tire developing a tread seperation and should be checked right away. A simple balance of the tire and wheel assemblies may be all that required also but when on a balancer they should be able to tell if the tire has a more severe problem.
Driveline components could cause vibrations also however if the above sounds like it fits then check that 1st.

check ur sway bar. the bolt probably came out, look at the front wheels behind the brake disk, you'll see the sway bar

Your Tires are Out of Balance. Get them Rotated and Balanced, Should fix Ya right up!