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Upon fitting a measurement model using the lavaan package in r and removing some low factor loadings, I noticed that one of the items / manifest variables has an insignificant variance (p = .418) This variable is the reference for the construct (market method) and the variance of the construct is significant (p = .004). If it wasn't, I am aware that it would indicate the item would be insignificant.

The model concerns a two factor model with 4 items loading on factor1 and 2 items loading on factor 2. The insignificant variance I talk about is of one of the two items that loads on factor 2.

The overall model fit itself is also really bad. I was simply wondering the following: if my model fit would be good (i.e. several overall fit indices beyond their thresholds, good residuals, low / no modification indices) and I saw an insignificant variance such as this pop up. What does it indicate?

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A non-significant variance is probably not an issue. If the error variance is nearly zero, then it is possible that the estimate may be flagged as non-significant. The interpretation would be that the latent variable very-nearly perfectly predicts the item that is loading on that factor.

If you are seeing poor model fit, this "perfect" alignment of the latent construct and a single manifest may be part of the cause.

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