TN 385 from I-240 to I-269 at least wouldn't be up to current Interstate standards I think; there are some curves that are too sharp (the 90 degree turn north of Winchester in particular) and the shoulders are too narrow. Plus I think the AADT added with I-22 traffic would require widening the 4-lane part. My guess, as Froggie suggests, would be truncating at I-269 or getting a waiver to "temporarily" truncate at the state line and putting the ball in TDOT's court.
As for Lamar, my understanding is they do plan to add interchanges at Shelby Drive and Holmes Road but leave some at-grades in place. It'd be nice if they extended full control of access to Winchester at least (and NW of there to I-240 it's all depressed property that could be relocated if TDOT had the cash) but there's a lot of warehouse traffic that uses the at-grade accesses. Probably the best you might see is RIRO.
As for TDOT's "lack of enthusiasm" for I-69, it's more the northern part of 8 that isn't really justified based on traffic now (and being stuck with a half-finished SIU 7 that they need to finish to justify the hardly-used stuff that's already built, which they started because it was all that had gotten environmental clearance when they had the money). SIU 9 has fairly immediate need, and suburban growth is finally getting up towards Covington (hence the TN 14 widening parallel to US 51 to the east), justifying SIU 8 up to the Hatchie River or so - once you get north of there, the towns are effectively bypassed except Dyersburg proper. And TDOT is probably going to be done with I-269 (except the stub to I-69 at Millington, which is pointless to build except as part of the I-69 contract) before MDOT meets up.