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Constructing all NE-lattice paths from $(0,0)$ to $(m,n)$

If I consider only Dyck Paths, I can do write something like this:

DWS=DyckWords(3).list()
for D in DWS:
    print(D.height())

to obtain the height of all Dyck paths of length $3$. However, I would like to do the same thing but using $NE$-lattice paths from $(0,0)$ to $(m,n)$. Is there an easy way to do this in Sage?

Constructing all NE-lattice paths from $(0,0)$ to $(m,n)$

If I consider only Dyck Paths, I can do write something like this:

DWS=DyckWords(3).list()
for D in DWS:
    print(D.height())

to obtain the height of all Dyck paths of length $3$. However, I would like to do the same thing but using $NE$-lattice paths from $(0,0)$ to $(m,n)$. Is there an easy way to do this in Sage?

Constructing all NE-lattice paths from $(0,0)$ to $(m,n)$

If I consider only Dyck Paths, I can do write something like this:

DWS=DyckWords(3).list()
for D in DWS:
    print(D.height())

to obtain the height of all Dyck paths of length $3$. However, I would like to do the same thing but using $NE$-lattice paths from $(0,0)$ to $(m,n)$. Is there an easy way to do this in Sage?