Instead of scaling the Legos up, assume that they're life size beings on a Lego sized pseudo-Earth. It's been years since I've done any physics so, I hope I'm not badly off, but I think the gravity will be around 1/900th that of Earth (if we assume radius of Lego world at 1/30 earth, mass of Lego world proportional to the cube). If we ignore the fact that there probably won't be an atmosphere on Lego world, I'm sure there are are various other applications of the square-cube law, etc. that will work in their favor as well.

I believe they'll make it.

It'll actually still be 1/30th of the Earth, since from Newton's law of universal gravitation:

F = G * (m_1 * m_2) / r^2

m_2 * a = G * (m_1 * m_2) / r^2

a = G * m_1 / r^2

If we make m_1 1/30th of its original size and to the same to r:

a = G * (m_1 / 30^3) / (r / 30)^2

a = G * (m_1) / r / 30

As escape velocity v_e is where GPE + KE = 0:

v_e = sqrt(2 * g * r) from the surface of the planet

If g is now 1/30th of it's original amount as shown above, the escape velocity would be sqrt(30) = 5.477 times less, or about 2042 m/s. So yup, they would make it if it's at 1/30th the size of the Earth, with thrust to spare for air resistance.

I'm sure there's a city with train services connecting Dublin, CA (served by the BART) to Moscow, ID. The question might just be when...

There is an underwater-tunnel between france and england with trains running. And there is the irish sea bridge-project with the goal to connect great britain and ireland by train and cars. Making such a route possible in some yet unbuild future reality.