Conversion of RE to NFA I've a question regarding this diagram. I'm thinking of adding a new state between q5 and q6 that accepts a lambda value but I'm not quite sure or this diagram is correct?
And in what situation we add a state that accepts an epsilon/lambda?
RE:1*(00|011*)*00
An epsilon transition (also epsilon move or lambda transition) allows an automaton to change its state spontaneously, i.e. without consuming an input symbol.
You need them for two cases
$1.$ The string or part of the string includes a Kleene star $^*$. E.g. $(10)^*$
$2.$ We have the option to choose between different strings. E.g. $0|1$
Now to make the string $$1^*(00|011^*)^*00$$ much easier, we will split the string in different steps.
Step $1$: Find NFA for $1^*$. We can do this by the following

Step $2$: Find $(00|011)^*$. We will skip $1^*$ to make it ourself easier.

Step $3$: Now we add $1^*$ to the previous NFA. We actually can 'substitute' the DFA in step $1$.

Step $4$: Make sure the string ends with $00$.

If we combine the previous steps, we get the following

You also can always check your answers by a RE to DFA/NFA converter.
Note: The above NFA is made inductivly and can be reduced by removing $\epsilon$ transitions as it is not necessary.