Hello. I can input using Mathematica each of the following:

Input[1]
LXi = {
E^(1/2  t  Sqrt[\[Kappa]]  Sqrt[8 \[Theta] + \[Kappa]])  Sqrt[x]
C[1] , 0 * C[1] };
LPhi = {((
E^(1/2  t  Sqrt[\[Kappa]]  Sqrt[8 \[Theta] + \[Kappa]]) u Sqrt[
x])/(4 \[Theta]) + (
E^(1/2  t  Sqrt[\[Kappa]]  Sqrt[8 \[Theta] + \[Kappa]]) u Sqrt[
x] Sqrt[8 \[Theta] + \[Kappa]])/(4 \[Theta] Sqrt[\[Kappa]]))*
C[1] + g[x, t]};
Input[2]                EDsI = SubstInfinitesimals[EDs, LXi, LPhi]

Out[2]= {0, 0, 0, 0, 0, 0, -x g[x, t] + 
\!\(\*SuperscriptBox[\(g\), 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "1"}], ")"}],
Derivative],
MultilineFunction->None]\)[x, t] - x \[Kappa] 
\!\(\*SuperscriptBox[\(g\), 
TagBox[
RowBox[{"(", 
RowBox[{"1", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[x, t] + \[Theta] \[Kappa] 
\!\(\*SuperscriptBox[\(g\), 
TagBox[
RowBox[{"(", 
RowBox[{"1", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[x, t] + 2 x \[Theta] \[Kappa] 
\!\(\*SuperscriptBox[\(g\), 
TagBox[
RowBox[{"(", 
RowBox[{"2", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[x, t]}

Another one:

Input[3]
LXi = {
       E^(-(1/2)  t  Sqrt[\[Kappa]]  Sqrt[8 \[Theta] + \[Kappa]])  Sqrt[x]
           C[2] , 0 * C[2] };
    LPhi = { ((
           E^(-(1/2)  t  Sqrt[\[Kappa]]  Sqrt[8 \[Theta] + \[Kappa]])
             u Sqrt[x])/(4 \[Theta]) - (
           E^(-(1/2)  t  Sqrt[\[Kappa]]  Sqrt[8 \[Theta] + \[Kappa]])
             u Sqrt[x] Sqrt[8 \[Theta] + \[Kappa]])/(
           4 \[Theta] Sqrt[\[Kappa]]))*C[2] + g[x, t]};
In[4]:= EDsI = SubstInfinitesimals[EDs, LXi, LPhi]

    Out[4]= {0, 0, 0, 0, 0, 0, -x g[x, t] + 
    \!\(\*SuperscriptBox[\(g\), 
    TagBox[
    RowBox[{"(", 
    RowBox[{"0", ",", "1"}], ")"}],
    Derivative],
    MultilineFunction->None]\)[x, t] - x \[Kappa] 
    \!\(\*SuperscriptBox[\(g\), 
    TagBox[
    RowBox[{"(", 
    RowBox[{"1", ",", "0"}], ")"}],
    Derivative],
    MultilineFunction->None]\)[x, t] + \[Theta] \[Kappa] 
    \!\(\*SuperscriptBox[\(g\), 
    TagBox[
    RowBox[{"(", 
    RowBox[{"1", ",", "0"}], ")"}],
    Derivative],
    MultilineFunction->None]\)[x, t] + 2 x \[Theta] \[Kappa] 
    \!\(\*SuperscriptBox[\(g\), 
    TagBox[
    RowBox[{"(", 
    RowBox[{"2", ",", "0"}], ")"}],
    Derivative],
    MultilineFunction->None]\)[x, t]}

Another one:

Input[5]
LXi = {(*Xi[1][x,t]*)
   E^(1/2  t  Sqrt[\[Kappa]]  Sqrt[8 \[Theta] + \[Kappa]])  Sqrt[x]
       C[3] ,(* Xi[2][t]*) 0 * C[3] };
LPhi = {(* f[x,
   t]u *) ((
       E^(1/2  t  Sqrt[\[Kappa]]  Sqrt[8 \[Theta] + \[Kappa]]) u Sqrt[
        x])/(4 \[Theta]) + (
       E^(1/2  t  Sqrt[\[Kappa]]  Sqrt[8 \[Theta] + \[Kappa]]) u Sqrt[
        x] Sqrt[8 \[Theta] + \[Kappa]])/(4 \[Theta] Sqrt[\[Kappa]]))*
     C[3] + g[x, t]};
   Input[6] EDsI = SubstInfinitesimals[EDs, LXi, LPhi]

From the last input I will still obtain the same output as the rest of above inputs. That means if I first substitute each into LXi={ some expression * Ck , some expression * Ck} LPhi={ some expression * Ck + g[x,t]} and then run EDsI = SubstInfinitesimals[EDs, LXi, LPhi] I keep getting the same answer, regardless what is defined as SubstInfinitesimals or EDs.
I attempted to do the same repeated operation all at once, however, I am not obtaining the output

Output[7]= {0, 0, 0, 0, 0, 0, -x g[x, t] + 
    \!\(\*SuperscriptBox[\(g\), 
    TagBox[
    RowBox[{"(", 
    RowBox[{"0", ",", "1"}], ")"}],
    Derivative],
    MultilineFunction->None]\)[x, t] - x \[Kappa] 
    \!\(\*SuperscriptBox[\(g\), 
    TagBox[
    RowBox[{"(", 
    RowBox[{"1", ",", "0"}], ")"}],
    Derivative],
    MultilineFunction->None]\)[x, t] + \[Theta] \[Kappa] 
    \!\(\*SuperscriptBox[\(g\), 
    TagBox[
    RowBox[{"(", 
    RowBox[{"1", ",", "0"}], ")"}],
    Derivative],
    MultilineFunction->None]\)[x, t] + 2 x \[Theta] \[Kappa] 
    \!\(\*SuperscriptBox[\(g\), 
    TagBox[
    RowBox[{"(", 
    RowBox[{"2", ",", "0"}], ")"}],
    Derivative],
    MultilineFunction->None]\)[x, t]}

So can you please help me to do the same repeated operation all at once and still obtain that same output