No
Lagging tail makes you go last. It does not reduce your speed. This means you will always go last in your priority bracket, regardless if Trick Room is up or not.
Iron Ball on the other hand, halves your speed, so it's probably what you're thinking of.
Do note that sometimes, your fastest Pokemon will still end up outspeeding them, and because of that end up going last in Trick Room. Take for example, Jolteon who's lowest possible speed is 238. Give it an Iron Ball, its speed stat drops down to 119. Escavalier on the other hand, has a bottom speed of 40. It remains slower than Jolteon, so Trick Room will still work in its favour.
It is also not suggested to slow down your own Pokemon just for the purpose of beating Trick Room. If you do so, you seriously disadvantage yourself against any other type of team, which combined together are probably more common than Trick Room.
There are better ways to try counter Trick Room including running Trick Room yourself, using Priority and having a defensive core which can switch in and out of the opponent's attacks and delay out the Trick Room. Running slow Pokemon like Escavalier who work outside of Trick Room is also fine, since it can use the effects of Trick Room a well.
My advice would be to rebuild if you're really worried about those Trick Room teams. Change your team a little, build a defensive core that walls most of the Trick Room abusers, and so on. You can also try using Lead Pokemon with Taunt in order to prevent the setting up of Trick Room.
