Is Tetrahydrofuran viable for dissolving PLA and sticking PLA objects together? According to Wikipedia, Tetrahydrofuran dissolves PLA. It also apparently dissolves PET.


  THF is considered a relatively nontoxic solvent, with the median lethal dose (LD50) comparable to that for acetone.


Wikipedia further states that it's not particularly dangerous provided you keep it away from air circulation, so that it does not form peroxides.


  One danger posed by THF follows from its tendency to form highly explosive peroxides on storage in air.


So well, this seems acceptable compared to other possible solvents which are all ridiculously dangerous. The question at hand is now of practical nature:


Is Tetrahudrofuran actually viable replacement for acetone, which only works with ABS?


I am asking because the fact that it does dissolve PLA does not really at all mean that it will work well. It could damage PLA structure, be more toxic than wikipedia says or not dry well.
According to Shuichi Sato, Daiki Gondo, Takayuki Wada, Shinji Kanehashi &amp; Kazukiyo Nagai: Effects of various liquid organic solvents on solvent‐induced crystallization of amorphous poly(lactic acid) film in Journal of Applied Polymer Science, Volume 129 Issue 3 (2013), p1607-1617source, Tetrahydrofuran is classified as a solvent for PLA. The specific entry on page 1608:
Group  Solvent          Solvent type    dd   dp   dh   dt   Result
Ether  Tetrahydrofuran  Polar aprotic  16.8  5.7  8   19.4  soluble

The values dd dp dh and dt are explained on page 1607:

The effects of 60 liquid organic solvents on PLA are systematically
investigated using the Hansen solubility parameter (HSP). The HSP
is one of the digitizing methods for analyzing the interaction
between polymer materials and organic solvents. In HSP analysis,
all solvents have three parameters: energy from dispersion bonds
between molecules (dd), dipolar intermolecular force between molecules
(dp), and the hydrogen bonds between molecules (dh). All solvents
were characterized by a point in a three-dimensional structure
at which dd, dp, and dh are plotted on three mutually perpendicular
axes. Generally, if the HSP values of the various organic solvents
are near that of the given polymer, the solvent is considered compatible
with the polymer material.

The factor dt is the total Hansen solubility parameter - the bigger this is, the better it is a solvent.
19.4 is a rather good solvent but extremely explosive: in air 20000 ppm (2%) are explosive and thus the allowable concentration in an area is 2000 ppmsource
Alternatives
A similar potent solvent would be Benzene (dt = 18.6) which more easily available and less explosive, but more deadly (10000-20000 ppm fumes) and has an allowable concentration of 500 ppmsource
Ethyl-acetate is also a solvent (dt = 18.2) and more available. It is explosive at an equal concentration as Tetrahydrofuransource, but it has just about half of its vapor pressure (73 mmHgsource  vs. 132 mmHgsource), so can be stored more safely, and is less aggressive on the body. It is sometimes used to Smooth PLA via vapor chambersource, and only comes at a price tag of ca. 90 €/l for the pure stuff and also is used in some nail polish removers, put into a safe mix.
Acetone is classified as a better solvent (dt = 20.1), and it is known to act as a glue and to soften PLA with some exposure time, but from experience, it can't smooth it. It is available most easy (nail polish remover and in the home depot), and is the least deadly option.
Propylene-1,2-carbonate is classed as solvent and a far better at it with dt = 27.2. It has been used as an alternative to Ethyl-Acetatesource and its MSDS is rather gentlesource. It comes at a price tag of 130 €/l for the chemical-grade liquid.
Conclusion
Tetrahydrofuran is not a viable replacement due to its explosive properties. It is not an improvement above Benzene, which at least can be stored safely.
Using Acetone as a benchmark, Tetrahydrofuran should not smooth the surface in a vapor chamber, as it is a worse solvent than Acetone. It should also take longer to soften and dissolve objects than Acetone, but a heated bath or coating the surface with it could help to generate the needed exposure times.
However, its comparable ethyl-acetate has been claimed to be used as a cleaning, vapor smoothing, and brush on surface smoothing agent successfully and can be used better by helping the solubility via heating, which can be done much safer with ethyl-acetate than THF. In a proper chemical mix, its storage problem can be solved too.
A better alternative is propylene-1,2-carbonate, which is a better solvent, and much less dangerous.
tl;dr: No, Tetrahydrofuran is not able to dissolve PLA in a reasonable time1 without heat activation and it has worse characteristics than Acetone. It could arguably be used to weld parts, but Dichloromethane would be more effective.

1 - Sato, Gondo et al. in the aforementioned paper: Solubility tests were performed for 24 h at 35+-1 °C. which means we have a prolonged exposure of a thin film to a huge amount of solvent. how thin a film? Very thin: The PLA films
were prepared by casting 2 wt % dichloromethane solution onto a
flat-bottomed glass Petri dish in a glass bell-type vessel and by drying
under atmospheric pressure at room temperature. Each solvent
was allowed to evaporate for 48 h. The dried PLA films were then
thermally treated under a vacuum for 48 h at 70 °C to eliminate
the residual solvent and to obtain amorphous PLA films. Afterwards,
the thermally treated PLA films were cooled at room temperature
under atmospheric pressure.