A very easy way to do this is to use multiprocessing alongside cvxpy. It won't be fastest possible, but since you want to stick to Python and avoid low level C/C++/Fortran code it's clear that you intend to leave some performance on the table for ease of implementation (and I don't blame you).
Here's an example of how to do it, taken from the cvxpy documentation. This solves a Lasso problem for various values of the penalty parameter, but the extension to LPs should be clear.
import cvxpy as cp
import numpy
import matplotlib.pyplot as plt
# Problem data.
n = 15
m = 10
numpy.random.seed(1)
A = numpy.random.randn(n, m)
b = numpy.random.randn(n)
# gamma must be nonnegative due to DCP rules.
gamma = cp.Parameter(nonneg=True)
# Construct the problem.
x = cp.Variable(m)
error = cp.sum_squares(A @ x - b)
obj = cp.Minimize(error + gamma*cp.norm(x, 1))
prob = cp.Problem(obj)
from multiprocessing import Pool
# Assign a value to gamma and find the optimal x.
def get_x(gamma_value):
gamma.value = gamma_value
result = prob.solve()
return x.value
# Parallel computation (set to 1 process here).
pool = Pool(processes = 1)
x_values = pool.map(get_x, gamma_vals)